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@mmore500
Created January 18, 2022 17:57
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pareto.ipynb
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{
"nbformat": 4,
"nbformat_minor": 0,
"metadata": {
"colab": {
"name": "pareto.ipynb",
"provenance": [],
"collapsed_sections": [
"sJBTsXJCSEql"
],
"authorship_tag": "ABX9TyNfptDGlCXGMc6jLIJn1Nix",
"include_colab_link": true
},
"kernelspec": {
"name": "python3",
"display_name": "Python 3"
},
"language_info": {
"name": "python"
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"<a href=\"https://colab.research.google.com/gist/mmore500/b6de0158a8851ce6e3d65105ed35197f/pareto.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"id": "31_tHHnsMMBR"
},
"outputs": [],
"source": [
"from matplotlib import pyplot as plt\n",
"import numpy as np\n",
"import pandas as pd\n",
"from scipy import stats\n",
"import seaborn as sns"
]
},
{
"cell_type": "code",
"source": [
"def bounded_pareto_pdf(x, *, alpha=1.0, lower_bound=1.0, upper_bound=float('inf')):\n",
" return alpha * lower_bound**alpha * x**(-alpha-1) / (1 - (lower_bound / upper_bound)**alpha)"
],
"metadata": {
"id": "D42lifkhh9xj"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"def bounded_pareto_cdf(x, *, alpha=1.0, lower_bound=1.0, upper_bound=float('inf')):\n",
" return (1 - lower_bound**alpha * x**(-alpha)) / (1 - (lower_bound/upper_bound)**alpha)"
],
"metadata": {
"id": "lVioq-R3ipsP"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"def pareto_inverse_transform_sample(*, alpha=1.0, lower_bound=1.0):\n",
" return lower_bound / stats.uniform.rvs()**(1.0/alpha)"
],
"metadata": {
"id": "LMvbUKvyjsu_"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"def bounded_pareto_inverse_transform_sample(*, alpha=1.0, lower_bound=1.0, upper_bound=float('inf')):\n",
" unif_lb = (lower_bound / upper_bound)**(alpha)\n",
" unif_ub = 1.0\n",
" unif_scale = unif_ub - unif_lb\n",
" return lower_bound / stats.uniform.rvs(loc=unif_lb, scale=unif_scale)**(1.0/alpha)\n",
" \n",
" # equivalent to\n",
" # https://www.wolframalpha.com/input/?i=inverse+f%28x%29+%3D+%281-L%5Ea*x%5E-a%29%2F%281+-+%28L%2FH%29%5Ea%29\n",
" # opp_lb_ub_alph = 1 - (lower_bound/upper_bound)**alpha\n",
" # return ( -lower_bound**(-alpha) * opp_lb_ub_alph * (stats.uniform.rvs() - 1 / opp_lb_ub_alph) ) ** (-1/alpha)\n",
"\n",
" # but this formula from Wikipedia appears to be wrong\n",
" # https://en.wikipedia.org/wiki/Pareto_distribution#:~:text=Generating%20bounded%20Pareto%20random%20variables%5Bedit%5D"
],
"metadata": {
"id": "f_1MyCw9kaU9"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"def bounded_pareto_rejection_sample(alpha=1.0, lower_bound=1.0, upper_bound=float('inf')):\n",
" while True:\n",
" sample = pareto_inverse_transform_sample(alpha=alpha, lower_bound=lower_bound)\n",
" if sample < upper_bound:\n",
" return sample"
],
"metadata": {
"id": "eQ9cskeVwG-f"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"source": [
"# np.random.pareto (known generator)"
],
"metadata": {
"id": "VseEvxEjRfFd"
}
},
{
"cell_type": "markdown",
"source": [
"### Cumulative Density Function"
],
"metadata": {
"id": "ZiIy8lBySF37"
}
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from np.random.pareto\n",
" data = pd.DataFrame.from_records([{\n",
" 'sample' : 1 + np.random.pareto(alpha),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='sample', kind='ecdf')\n",
"\n",
" #expected\n",
" x = np.geomspace(data['sample'].min(), data['sample'].max(), 100)\n",
" plt.gca().plot(x, stats.pareto.cdf(x, alpha),'r-', lw=5, alpha=0.6)\n",
"\n",
" plt.gca().set(xscale=\"log\")\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "pVQGO3n3MNQK",
"outputId": "dc62e4d2-b863-4ffa-f4c2-f0579a43b889"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"### Probability Density Function"
],
"metadata": {
"id": "sJBTsXJCSEql"
}
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" data = pd.DataFrame.from_records([{\n",
" 'logsample' : np.log(np.random.pareto(1.0) + 1),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='logsample', kind='kde')\n",
"\n",
" x = np.linspace(data['logsample'].min(), data['logsample'].max(), 100)\n",
" plt.gca().plot(x, stats.pareto.pdf(x, 1.0),'r-', lw=5, alpha=0.6, label='pareto cdf')\n",
"\n",
" plt.gca().set(yscale=\"log\")\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "GcLQUIXqMNWd",
"outputId": "6cda8edf-0151-4cc4-e6ef-522caef8ecc2"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"# scipy.stats.pareto (known generator)"
],
"metadata": {
"id": "giXj4kbtcXIl"
}
},
{
"cell_type": "markdown",
"source": [
"### Cumulative Density Function"
],
"metadata": {
"id": "1KgBgvOQcePC"
}
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from scipy.stats.pareto\n",
" data = pd.DataFrame.from_records([{\n",
" 'sample' : stats.pareto.rvs(alpha),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='sample', kind='ecdf')\n",
"\n",
" #expected\n",
" x = np.geomspace((data['sample'].min(), data['sample'].max()), 100)\n",
" plt.gca().plot(x, stats.pareto.cdf(x, alpha),'r-', lw=5, alpha=0.6)\n",
"\n",
" plt.gca().set(xscale=\"log\")\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "KGPkY_nSce7R",
"outputId": "933fa589-7e4b-466e-ae8d-398c9a16ed71"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"### Probability Density Function"
],
"metadata": {
"id": "GsjUuD6ecwGz"
}
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from scipy.stats.pareto\n",
" data = pd.DataFrame.from_records([{\n",
" 'logsample' : np.log(stats.pareto.rvs(alpha)),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='logsample', kind='kde')\n",
"\n",
" #expected\n",
" x = np.linspace(data['logsample'].min(), data['logsample'].max(), 100)\n",
" plt.gca().plot(x, stats.pareto.pdf(x, alpha), 'r-', lw=5, alpha=0.6, label='pareto cdf')\n",
"\n",
" plt.gca().set(yscale=\"log\")\n"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "oUH2PkAscx4c",
"outputId": "3f3af0de-a485-4a09-a35a-7c57eaeed064"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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Pv3pjhU4d7wr69IH/+7/WF2dasgT+/GdrAowKGleFdCgfHK7dWUl2UgzJcZG23ytcTR6Ww83HF/DSokLunr1ag7orSEuzVtEbOdL/+e3b4U9/glWrQluXi7kqpENpXXEV/bISnC7DcT85uT+XTejJI3M38sCH650uR4VCdLS1JdcZZ/g/X10N998P77+v/dRBoCHdDk1Nhg0lVRRkakiLCL87cwjnjcrj3jlreeCDddqi7gpE4Mwz4brr/C9nagy88go88QTU1YW+PhdxZD3pzm5nRQ376hrpm6EhDdYaH38+byiNTU3cM2ct2/bs54/nHEGkV9sArjd6tDX55cEHrY1tW1q4EIqK4MYbIT099PW5gP4UtcOGkioADekDRHg93HvhiP/1UV/11EL27tOpw11CXh784hfWPor+bNsGd94JK1aEti6XcFVIh2p0x4ZiX0hn+lmIpgvzeKydXf5y/jDmbSzj9H98yqLNu50uS4VCQgL88IfWanr+7NsH//ynjqduB1eFdKhGd2woqSYxJoKMBPev2dEeF47J59Ubj8LrES56dB7/+GCd7pfYFXi91rrUV19tzVZsyRhrPPUDD1gPF1VAXBXSobKhpIq+GQldZs2O9hiRn8I7txzNGUO7c++ctVz4yJdsKdMfzC5h/HhrJT1/u5IDfPMN/PGP1vof6rA0pNuhOaTVoSXGRHL/1BHcd9EI1hVXcdr9n/Lv+Vt19EdXkJ8Pv/wlDBni//zu3fDXv1qb3urfh0PSkG6jypp6dlXUan90gESEs0fm8t6PjmFkjxR+8fpypj+ziOJKXfPD9eLj4eabW1+gqaEBXnzRGqZXo38fWqMh3UabSq3/svdJ15Z0W+SkxPLc1eP59eTBfL6+lFP+Ppf3V+oGp67n8VgLNN18s7VDuT8LF1qzFLdtC21tnYSGdBttLtsHQO90bUm3lccjXH10b9655WhyUmK55tlF3P/+Opqa9L+7rjd0KNxxB/Ts6f/8rl3WhreffabdHy24KqRDMQRvs68l3SO1lVaBOqyCzET+c+NRnDsyl7+/v5abXlhMdW2D02Upu6WlwW23wbHH+j9fXw/PPWftpajdH//jqpAOxRC8zaXVdE+OITbKa9s9uoKYSC/3XDicX00ezH9X7uSKJxdQWaOTX1wvMhIuvtjaTCC6lSGs8+dbk18KdfcfcFlIh8Lmsmp6pmkrOhhEhOlH9+afF49iaWE5lz2xgL37Nai7hHHjrFmKOTn+zxcXW90fH33U5bs/NKTbaHPZPu2PDrLTh3bnwUtG8c2OvVzy+DwqtEXdNWRnW+tTT5zo/3xDA8yYAQ891KUnv2hIt8He/fXsrq6jV5qGdLCdPCSbRy8bw+qiSr7/wmLqdYZi1xAVBZdfbs1SbK37Y9ky+P3vYe3a0NYWJjSk26B5xlxPDWlbHD8wkzvPOYJP15Xym7e+0UkvXcn48dbkl9Z2fSkvh3vvhTfegMbG0NbmMA3pNmgeI63dHfa5aGwPbjyuL/+ev5XHPt3odDkqlLKy4Pbb4fjj/Z83BmbPtnYoLykJbW0O0pBugy2+MdI6/M5et508gDOGdueu2av5ZG3X+WFUWKM/pk611p9ubfLL5s3whz/AF190iYeKGtJtsHX3PrKSonX4nc08HuGvFwxjQFYit7y4hK2+fxxVFzJiBPz619Cvn//ztbXwzDPw2GOuf6ioId0GW3fvI7+btqJDIS4qgkcuG40xhuuf/4r9dV2rH1IB3brBj39sbdPlaSWqvvrKeqjo4o1vXRXSds843LZ7n3Z1hFDPtHjunzaS1Tsr+L/XvtYHiV2Rx2NteHvbba1vv1VeDvfdBy+/bM1adBlXhbSdMw5rGxopqqghX0M6pI4fkMmPT+rPG0t38NTnm50uRzmlTx/41a9gwoTWX/PBB9ZMxa1bQ1dXCLgqpO20o7wGY9CQdsD3jy/ge4OzuHPWKuZt9LPZqeoaYmLgqqvgmmsgNtb/a4qK4K67YNYsaHLHWHsN6QBt3a0jO5zi8Qj3XDicnqlx3Pzvxewo3+90ScpJY8daDxX79/d/vqkJ3nzTGqq3q/Mvh6shHaBCX0jnp7byL7iyVVJMJI9ePpra+iYufXw+JZW1TpeknJSaaj1UPP98iIjw/5pNm6yheh980KmH6mlIB6hw9z6ivB6yEmOcLqXLKshM5KmrxlK0t4aLHv1Sh+Z1dSLwve9ZCzW1NlOxvt56oHjPPVBaGtr6gkRDOkCFe/aRlxqLx6ObzzppTK9Unrl6HGVVdZz94OfM0d1dVG6utVDTaadZwe3PunXWUL1OuKeihnSAdIx0+BjXO5XXbzqKrKQYrn12Edc+u4gV2+3b6EF1AhERcPbZ1lC9zEz/r6mttfZU/PvfO1WrWkM6QNv27Cevm/ZHh4s+GQm8+f2J3HbKAOZtLGPyA59x3kNf8PqSbdTU68SXLqtvX2ubrtbW/wBYs8ZqVXeStao1pAOwr66B8n315GpIh5WoCA/fP76Az352AnecMYjd1XXc+tIyjrzrA+6evZo91XVOl6icEB1trf9x663Wll3+1NZaa1Xfc4+1wUAY05AOwI5ya7+13BQN6XCUHBfJNZP68OFPjuWFa8YzoU8aj87dwDF//YgZC7bqTMWuauBAa6jepEmtv6a5r/r998O2Va0hHYDmcbk5GtJhTUSYWJDOQ5eO5t0fHcMROcnc/tpyfvDiEmobtAukS4qJgUsvhR/9yFoLxJ/6+rDeUEBDOgDNId09WYffdRb9sxJ54Zrx3HbKAGZ+XcRVTy3URZq6skGD4Le/hWOOOfhcXBxccknrI0McpiEdgB3l+/EIZCVpSHcmHo/w/eMLuOeC4Xy5sYxbZiyhsSk8/0urQiAmxgrjln3VF14INqz3EyxhH9Ii0kdEnhCRV52qYXt5DVlJMUR6w/6PS/lx3ug8fjN5MHNW7uIv7612uhzltIED4Te/sUaADB166EWbwoCtqSMiT4pIsYisaHH8VBFZIyLrReT2Q13DGLPRGDPdzjoPZ0f5fu2P7uSunNibi8f34JFPNupuL+rbESA33RS23RzN7G4aPg2ceuABEfEC/wJOAwYD00RksIgMFZGZLT5aGZUeWjv2aki7wa8nD2ZAViI/eXkZe/e5b91h1Q6tbSYQRmyt0BgzF9jd4vA4YL2vhVwHzADOMsYsN8ZMbvHh+ADGpiZDUXkNOSnaH93ZxUR6uefC4ezZV8fd79qwk0eYDuFSnZsT/4zkAoUHfL7Nd8wvEUkTkYeBkSLyf4d43XUiskhEFpUEcSfh0upa6hqbdIy0SxyRm8zVE3vx4oJCvtrSsv2gVPgJ+7a+MabMGHODMaavMeauQ7zuUWPMGGPMmIyMjKDdv3kiS06yhrRb/Oik/mQmRvPHd1bpRBcV9pwI6e1A/gGf5/mOdZgdexwW6UQW14mPjuCnJw9gydZy3lle5HQ5Sh2SEyG9EOgnIr1FJAqYCrwVjAvbscfh9v+FtPZJu8l5o/MYmJ3IvXPW6thpFdbsHoL3IvAlMEBEtonIdGNMA3Az8B6wCnjZGPONnXV0xI7yGuKivCTHRjpdigoir0f44Yn92FhSzcyvdzhdjlKtamXfmeAwxkxr5fgsYFaw7yciU4ApBQUFQbtm8xhpCfOxlKrtThmSzYCsRB74cD2Th+Xg1Q0dVBgK+weHbWFHd4eOkXYvj0f4wYkFrC+uYpb2Tasw5aqQtsOO8v3kan+0a51+RHf6ZSbwwIfraNK+aRWGNKQPoaa+kdKqOh1+52Iej3DzCQWs3VXFu9/sdLocpQ7iqpAO9hC8or2+MdLa3eFqk4fl0Ccjngc+XK/jplXYcVVIB7tPWhf77xq8HuH7xxWwqqiC91e1fyWC/XUNlFXXsl/3WFRB5KqQDrbmMdI6Jdz9zhqRQ4/UOB74cF2bW9Pb9uzjphe+Ytpj83hvxS5eX7yd/36zk5KqWpuqVV2JhvQhFJXXIAJZydFOl6JsFuH1cNNxffl6214+bsNSpvM2lnHafZ/y4epizh6Ry9H90hmen0JVbSNzVu5i3sYyG6tWXYGrQjrYfdI7yveTnhBNdIQ3KNdT4e3cUXnkpsTywAeBtaY/X1/K5U8uICs5hjm3HsuVE3vTIzWOITlJTBnenZzkWF5fsp2nP98UguqVW7kqpIPdJ72zokb3NexCoiI83HBcXxZvLefD1Yfum167q5IbnvuK3mnxvHL9keSnxn3nfKTXw6T+6QzpnsTvZ67kw9W77CxduZirQjrYdlXUkJmoId2VTB2bT9+MeP4wc2WrO4wXV9Zw1VMLiY3y8tRVY+kWH+X3dV4RLhqXz+CcJH40YylFe/fbWbpyKQ3pQyiurCUrSfuju5JIr4dfTxnC5rJ9PPjRhoPOV9bUM/3pRezZV8eTV4497Mif6Agv/5w2ioYmw89e/VonzKg2c1VIB7NPurahkd3VdbpDeBd0bP8Mzh2Zyz8+XMcHq77tpqiqbeCqpxayqqiCf148kiNyA+tW65Uezy/PGMSn60p5bt4Wu8pWLuWqkA5mn3RJpTV8SlvSXdOd5wxlcPckbnj+K+6evZqnP9/EKX+fy+Kte7h/6khOGJjVputdPK4Hxw/I4K7Zq1hfXGVT1cqNXBXSwbSrwgrpTG1Jd0mxUV6evXocZwztzsOfbOC3b68kNsrLS9cfyRnDurf5eiLCn88bRkykl9v/o90eKnC2LlXamRVXWFPCs/TBYZeVlhDNfVNHcvtpgzAYMhNjOrScaWZSDL84fRA/e/VrXl5UyNRxPYJYrXIrbUm3YldzSGt3R5eXnRxD9+TYoKw3fcHoPMb1TuWu2asp1RmJKgAa0q3YVVlLpFfoFud/eJVS7SEi/Omcoeyra+DOd1Y5XY7qBFwV0sEc3bGrooaMhGg8uluHCrKCzARuOLYvry/ZzufrS50uR4U5V4V0MEd3FFfU6kNDZZvvH19Az7Q47nhjBTW6ap46hIBCWkReE5EzRMRVoX4ouypqtD9a2SYm0ssfzz6CTaXVPPjxwZNmlGoWaOg+CFwMrBORu0VkgI01hQVrtqG2pJV9JvXL4KwROTz88QYdO61aFVBIG2PeN8ZcAowCNgPvi8gXInKViETaWaATauob2bu/XkNa2e6OMwYTE+nhjjeW664wyq+Auy9EJA24ErgGWALcjxXac2ypzEHFzRNZErW7Q9krIzGan582kHkbd/OO7liu/Ai0T/p14FMgDphijDnTGPOSMeYHQIKdBTphV2XzGGltSSv7TR3bg0Hdk7hr1mp9iKgOEmhL+jFjzGBjzF3GmCIAEYkGMMaMsa26NgrWELxvJ7JoSCv7eT3CryYPYnv5fp76fLPT5agwE2hI/9HPsS+DWUgwBGsIXvO6HTq6Q4XKUX3TOW5ABg9/soGKmnqny1Fh5JAhLSLZIjIaiBWRkSIyyvdxHFbXhysVV9QQFeEhOdZ1z0RVGPvJ9wawd389T36m222pbx1ugaVTsB4W5gH3HnC8EviFTTU5rnmMtIjONlShMzQvmZMHZ/HEZ5u4ZlIfEqJ1/TN1mJa0MeYZY8zxwJXGmOMP+DjTGPNaiGoMuV0Vtbr6nXLEjcf1pbKmgZcWFjpdigoTh/ynWkQuNcY8D/QSkR+3PG+MudfPl3V6uyprGJSd5HQZqgsa2aMb43ql8uRnm7j8yJ5EervMJF/VisP9DYj3/ZoAJPr5cCVr3Q59aKicce0xfdhevp/3V+oO4+owLWljzCO+X38XmnKcV1XbQFVtgw6/U445YWAmOckx/HvBVk4b2vZdYJS7BDqZ5S8ikiQikSLygYiUiMildhfnhGJd7F85zOsRLhrbg0/XlVK4e5/T5SiHBdrhdbIxpgKYjLV2RwFwm11FOel/Y6T1waFy0IVj8/AIzFi41elSlMMCDenmbpEzgFeMMR1fVT9MFfumhGuftHJS9+RYju6XwRtLdujCS11coCE9U0RWA6OBD0QkA6ixr6z2Cca08JJKqyWdoS1p5bCzhuewvXw/i7fucbqUoGhsMuzdX6//6LRRoEuV3g4cBYwxxtQD1cBZdhbWHsGYFl5SVUuU10NSjE4kUM46eUgW0REe3lq6w+lSOqShsYkHPljHUQ4TRikAAB1YSURBVHd/wPDf/Zdhv/sv//poPfWNTU6X1im0ZRDmQOAiEbkcOB842Z6SnFVaWUd6QpTONlSOS4yJ5KRBWcz8uojGps7Z+txX18B1z33FPXPWMjA7idtPG8j43qn89b01TH9mEQ0a1IcVUHNRRJ4D+gJLgea1FA3wrE11Oaa0qpZ0XUdahYlTj8jmneVFLC3cw+ieqU6X0ybGGH7+n+V8vKaYP559BJdO6GmdOLYvz8/bwh1vrOB3b6/kD2cf4WyhYS7Q/9OPAQabLtCZVFql22ap8HHsgAwiPMKclcWdLqSfn7eFt5ft4LZTBnwb0D6XTujJlrJqHvt0E6cdkc1RBekOVRn+Au3uWAFk21lIuCitqiUtPsrpMpQCICkmknG9U/lgVeeafVhcUcPds1dzTP8Mbjy2r9/X/OTkAeSmxPL7mSs7bXdOKAQa0unAShF5T0Teav6wszAnNDUZyqrqtLtDhZWTBmWxrriKLWXVTpcSsLvfXU19o+EPZw3B4/H/fCcm0ssvTh/E6p2VvL5ke4gr7DwCDenfAmcDfwLuOeDDVSpq6mloMqQnaEir8HHSoCwA3l9V7HAlgVm5o4LXFm9n+qTe9EyLP+RrTx+azYCsRJ78bJMOzWtFoEPwPsGaaRjp+/1CYLGNdTmitMoaI52eoN0dKnz0SIujX2ZCp+ny+NfH60mIjuCGY/x3cxxIRLj8qJ6sLKpg0RZ3jAcPtkDX7rgWeBV4xHcoF3jDrqKcUlJZB0CGtqRVmDlpcBYLNu1m7/7w3lprY0kVs5YXcdmRPUmOC2xno3NG5pIUE8EzX2y2t7hOKtDuju8DE4EKAGPMOiDTrqKc8r+WtPZJqzBz0qBMGpoMn6wtcbqUQ3rq881Eej1MP7p3wF8TFxXBOSNzmbNyF1W1DTZW1zkFGtK1xpi65k9EJAJrnLSrfNvdoSGtwsuI/G6kxkeFdZfHvroG3liynclDu7f5Z2jy8BxqG5rC+v05JdBx0p+IyC+wNqT9HnAT8LZ9ZTmjtKoWr0dI0Q1oVZjxeoTjB2Ty/qpdNDQ2EdHOHVuMMcxZuYtFW/ZQXdvAqB7dOH1od2KjvB2ucebXRVTWNjB1XI82f+3oHt3ITorh7WVFnDUit8O1uEmg3+nbgRJgOXA9MAu4w66inFJaWUdafFSrQ4aUctIJAzPZu7+eJYXl7fr6LWXVnP2vz7nuua94+ovNvLV0Bz95ZRkn3/cJX24o63B9Ly7YSt+MeMb26tbmr/V4hDOGdWfu2hIqasK73z3UAh3d0YT1oPAmY8z5xpjHQjn7UETOFpHHROQlEbFtzZDSqlrt6lBha1L/dCI8wgftGIq3dlcl5z/8JVt27+NvFwxn5e9OYdlvTuaFa8YT6fFwxZML+HB1+7saVu+sYMnWcqaN69HudW9OPSKbusYmPltX2u463OiQIS2W34pIKbAGWOPbleXXgd5ARJ4UkWIRWdHi+KkiskZE1ovI7Ye6hjHmDWPMtcANwEWB3rutdN0OFc6SYiIZ2yuVj1a3LaT3VNdx1VMLEeDl64/k/NF5RHg9eDzCxIJ0Xr9pIgOyE7nhucUsa2crfcaCQqK8Hs4bldeurwcYmZ9CYkwEn6wJ74ejoXa4lvStWKM6xhpjUo0xqcB4YKKI3BrgPZ4GTj3wgIh4gX8BpwGDgWkiMlhEhorIzBYfB44iucP3dbYoraojXaeEqzB2wsBM1uyqZNuewLbVMsbwk1eWUVxZw6OXj6F/1sH7RyfHRfLs1ePISIzm5hcXt3mY3/66Rl5bvI3ThmbTrQM/PxFeD0cXpDN3XYlObDnA4UL6MmCaMWZT8wFjzEbgUuDyQG5gjJkL7G5xeByw3hiz0TdqZAZwljFmuTFmcouPYl+L/s/AbGOM30k0InKdiCwSkUUlJW3/l9gYoy1pFfaOH2i1WQJtTb++ZDsfri7mF6cPYkR+Squv6xYfxT+mjaSovIY/zFzZpppmLS+ioqaBqWPb/sCwpWP7Z1C0t4Z1xVUdvpZbHC6kI40xB3UQGWNKgI4MgcgFCg/4fJvvWGt+AJwEnC8iN/h7gTHmUWPMGGPMmIyMjDYXVFXbQG1Dk842VGGtb0Y8PdPi+DCAkC7fV8ed76xiZI8Urjiy12FfP7pnN66Z1IdXv9rGgk0t21Wte3HBVnqnxzOhT8dX6Tumv/Wzq10e3zpcSNe181xQGWP+YYwZbYy5wRjzsB33KK2y3o4+OFThTMQaivfFhjL21zUe8rX3vb+OPfvquPPsoQGPWLrlxAJyU2K5443lAS3Iv25XJYu27GHauPygbJSRkxJLn/R45m/q+GgTtzhcSA8XkQo/H5XA0A7cdzuQf8Dneb5jHdKRPQ51IovqLE4YmEltQxNfbGh9FMTm0mqen7eFi8b2YHBOUsDXjouK4FeTB7N2VxUvLSo87Ov/vWArkV7p0APDlsb2SmXh5j006fKlwGFC2hjjNcYk+flINMZ0pLtjIdBPRHqLSBQwFejw0qcd2eOwtFJDWnUO4/ukkhgTwcyvi1p9zV/fW0NUhIdbv9evzdc/ZUgW43qncu9/11J5iDHL1bUNvLpoG6cd0Z20IP7cjOnVjb3767Vf2qd905baQEReBL4EBojINhGZboxpAG4G3gNWAS8bY76xu5ZD+XbdDu2TVuEtOsLLlOE5zF5R5Hfix5Kte3hneRHXTupDZjt2vRcR7jhjEGXVdTz48YZWX/fa4m1U1jZwxVG92nyPQxnX2+rbXrA58H5xN7M9pI0x04wx3Y0xkcaYPGPME77js4wx/Y0xfY0xdwbjXh3p7iipqkMEUuM0pFX4u2B0HjX1TbzTojVtjOFPs1aRkRjNdcf0aff1h+WlcO7IXJ74bBOFuw8e7tfUZHjmyy0MzU1mVI/WR420R4/UODITo1nYhoeXbmZ7SIdSh7o7qmpJjYtq95oISoXSiPwU+mUm8ML8Ld/pu31t8XYWbt7DrSf1Jz460KV5/PvpKQPwCPx+5sqDxi2/vmQ764uruPaYPkF5YHggEWFs71QW2tySrm9s6hTjsTWRfEordUq46jxEhOuP7cuK7RXMWGg94Nu5t4bfvf0N43qlMnVs/mGucHg5KbH8+Hv9mbNy13e2t9pf18jf/ruGYXnJTB7avcP38WdkfgpFe2sorqgJ+rW/2bGXKQ98xqBfvcvxf/uY2ctb79sPB64K6Y6O7tD+aNWZnDcqlyP7pHHX7FU88skGzn/4C+oam/jL+cOCtkjY9KP7MKZnN371xgo+W1dKfWMTP355KUV7a/jF6YNsW4xsuG/izbJtbf9ZPpSFm3dz4cNfUlJZy/RJvYmO8HLjC4t5c2n47rHoqpDuSHdHWXUdafHakladh4hw93lDyU2J5a7Zq2lqMvz72gn0Sj/0voJt4fUID1w8krxucVzx1ALG3vk+s1fs5FeTBzOhT1rQ7tPSkJwkPAJfb2vfWiL+7Ktr4EczlpKRGM0b35/I/502iJm3HM243qn8/D9fs6qoImj3CqaOdVq5iHZ3qM6oZ1o8s384iS1l+8hIjO5wP7Q/3ZNjeeXGI3nwow3s3V/PUX3TmDI8J+j3OVBcVAT9sxKD2pK+7/11bC/fzys3HEl2sjXqJdLr4cFLRnHK3+fyp1mreG76+KDdL1g0pLH62KrrGrW7Q3VKIhLU1rM/STGR3H7aQFvv0dKwvGT+u3IXxpgOP5wsrqzhqc83ceGYPMb2+u709fSEaG44ti93zlrFgk27/zcEMFy4qrujvX3SOttQqfAzPD+F8n31FO7e3+FrPT9vKw1NhpuOK/B7/tIJPUlPiOb+D9Z2+F7B5qqQbm+fdEJ0BL+ZMpjRPdu+o4RSyh7Dcq2Hh8u3d6zLo6a+kRfmbeGEAZmt/o8jNsrLlUf15PP1ZWwtC2wZ2FBxVUi3V7f4KK6a2Ju+GQlOl6KU8umXlYBHYM3Ojj3Qe++bnZRV13HVxEPvYH7uqDxE4D+Lt3XofsGmIa2UCksxkV56p8ezamdlh67zztdFZCVFc1TfQ49GyUmJZWLfdF5bsi2sFnfSkFZKha2B3ZNY04GQrqpt4OO1JZx2RPeAxnSfNzqXwt37Wbx1T7vvGWyuCumOTGZRSoWfQdmJbN29j6rahnZ9/QerdlHX0MTkYYHNjDxxUJa12W8b95G0k6tCuiOTWZRS4WdAtrUWdntb07OX7yQrKZpRPQIbFNDezX7t5KqQVkq5y8Bsa+Pc9oR0Q2MTn68v5YSBmW2avn7CwExW76xke3nHh/4Fg4a0Uips5XWLJSE6gtXtGOGxbFs5lbUNTOrXtj1PTxhkbfYbyD6SoaAhrZQKWyLCgOxEVhe1vSU9d20pHuGwozpa6pMeT35qLJ+uDY/NcF0V0vrgUCn3GZidyOqdFW1e+/nTdSUMy0shpY0beYgI43unsXDz7rAYiueqkNYHh0q5z8DuSVTUNFC0N/C1pStq6llaWM6kfuntuuf43qns2VfP+hLn91l0VUgrpdyn+eFhW/qlF2/ZQ5Oh3cupju9tfd38jWXt+vpg0pBWSoW1Af8L6cD7pRdt3oPXI4zIb9/+i/mpsXRPjmF+GOyzqCGtlAprSTGR5KbEtunh4cLNuzkiJ6nd62uLCON6p7Jg027H90HUkFZKhb3mh4eBqG1oZGlhOWN6dWxd6NE9u1FcWcuONvSF20FDWikV9gZ2T2RjSTW1DY2Hfe2K7RXUNjQxtlfHlh4elmd1lXxdGLwtvNpDQ1opFfb6ZyXS0GTYVFp92Nd+tcXqRx7ds2Mt6UHdE4n0StA3w20rV4W0jpNWyp36Z1kPD9fuOvyQuKWF5eR1iyUjsWM7LUVHeBmYnRTUzXDbw1UhreOklXKnPhnxeD3Cul2Hf3i4rHBvu0d1tDQ8P5nl2/Y6OqnFVSGtlHKn6AgvPdPiWHuYkC6urGF7+f6ghfSwvBQqaxvYGEA3i100pJVSnUL/zETWHaa74+tCq6tzeLBa0nnN+yw61+WhIa2U6hT6ZyWwuayamvrWR3gsLSzH6xGOyAlOl2efjHiivJ52LfAULBrSSqlOoV9WIk0GNpa03vWwbFs5A7ISiY3yBuWekV4P/bISOrzPYkdoSCulOoXmER7riv0HZlOTYVlhedC6OpoNzE5idVHHdizvCA1ppVSn0Ds9nkivtLqGx6ayaipqGhgZ5JAe1D2R4spayqpqg3rdQGlIKxUsDq/x4HZRER76ZiSwqpVW7TLfzMBgt6QHdbf2WWzLAk/BpCGtlJ0k8L311OENzkli5Y7WQzo+yktBZkJQ79m8VGpr/zjYzVUhrTMOlXK3wd2TKK6spdRP18PSwnKG5iXjbcOms4FIS4gmMzGaVQ6N8HBVSOuMQ6XcrbnroWWrtrahkZVFFUHv6mg2IDux1QeWdnNVSCul3K21kF6xvYL6RhP0h4bN+mYksL64ypHp4RrSSqlOIzU+iuykmIO6HuZvsra5GtvBNaRbU5CZwL66RooqQr+2tIa0UqpTGZKTxLIWK9PN27ibAVmJpCV0bOW71jQ/jFxfHPqNaTWklVKdyoQ+aWwsqaZo734A6hubWLR5NxP62NOKBg1ppZQK2NH90gH4dF0pAMu372VfXWO7dwYPRFp8FClxkRrSSil1OAOzE0lPiOYzX0h/sd76dVxv+1rSIkJBRgIbNKSVUurQRISjC9L4fH0ptQ2N/Hv+Vsb1SrWtP7pZQWYC60s0pJVS6rCO6Z9BWXUd059exI69Ndx0fF/b71mQmcDu6jp2V9fZfq8DaUgrpTqdKcNzOHN4Dp+tL2VobjLH9s+w/Z59MuIBAtoMN5giQno3pZQKgkivh/suGsGEPmmM6dUNCcEaKb3SrJDeXFrN6J7dbL9fMw1ppVSn5PEIF4/vEbL75XWLwyOwuSy0LWnt7lBKqQBERXjI6xbH5rJ9Ib1v2Ie0iAwSkYdF5FURudHpepRSXVev9Hg2h7hP2taQFpEnRaRYRFa0OH6qiKwRkfUicvuhrmGMWWWMuQG4EJhoZ71KKXUovdPi2FxajQnhBg92t6SfBk498ICIeIF/AacBg4FpIjJYRIaKyMwWH5m+rzkTeAeYZXO9SinVql7p8VTWNlAWwmF4tj44NMbMFZFeLQ6PA9YbYzYCiMgM4CxjzF3A5Fau8xbwloi8A/zbvoqVUqp1B47wSLd58kwzJ/qkc4HCAz7f5jvml4gcJyL/EJFHOERLWkSuE5FFIrKopKQkeNUqpZRPr/TQj5UO+yF4xpiPgY8DeN2jwKMAY8aM0R1BlVJBl9ctFq9H2BLCER5OtKS3A/kHfJ7nO9ZhusehUspOkV4P3ZNjKNzj7pBeCPQTkd4iEgVMBd4KxoV1j0OllN16pMZRuNslIS0iLwJfAgNEZJuITDfGNAA3A+8Bq4CXjTHf2FmHUkoFS363OAr37A/Z/ewe3TGtleOzsGE4nYhMAaYUFBQE+9JKKQVAfmosJZW17K9rJDbKa/v9wn7GYVtod4dSym75qXEAbAtRv7SrQloppezWHNJbQ9QvrSGtlFJtkN/NCulQPTx0VUjrEDyllN3SE6KIjfSydXdoHh66KqS1T1opZTcRIT81NmRjpV0V0kopFQqhHCutIa2UUm2UmxLL9hCNlXZVSGuftFIqFHK7xVJZ20BFTb3t93JVSGuftFIqFHJSYgFC0pp2VUgrpVQo5PpCeke5hrRSSoWd3G6+lrSGdNton7RSKhTS46OJ8nq0u6OttE9aKRUKHo+QkxKjLWmllApXOSmxGtJKKRWuclNi9cGhUkqFq5yUWIora6lraLL1PhrSSinVDrndYjEGdu6tsfU+rgppHd2hlAqV5rHS28rtXcPDVSGtozuUUqGSlRQDwK4KbUkrpVTYyU62Qnrn3lpb76MhrZRS7ZAQHUFCdIS2pJVSKlxlJUXrg0OllApX3ZNj2aktaaWUCk9ZSTHa3dEWOgRPKRVK2cnRFFfW0thkbLuHq0Jah+AppUIpOymGxiZDWZV9IzxcFdJKKRVKzWOl7eyX1pBWSql2+nastIa0UkqFnewQzDrUkFZKqXZKS4jG6xGKtCWtlFLhx+sRMhOjtU9aKaXCVXayvWOlNaSVUqoDspNi9MGhUkqFK2vWoY6TDojOOFRKhVp2cgxVtQ1U1TbYcn1XhbTOOFRKhVrzMDy7ujxcFdJKKRVqdu/QoiGtlFIdYPesQw1ppZTqgGyb1+/QkFZKqQ6IjfKSHBupLWmllApX2Ukx2pJWSqlwlWXjrEMNaaWU6qBsGzek1ZBWSqkOyk6KobSqlobGpqBfW0NaKaU6KCMxmiYDu/fVBf3aGtJKKdVBGYnWMLxiG9bw0JBWSqkOykiMBqDEhg1pNaSVUqqDMptDWlvSSikVfrp8S1pE4kVkkYhMdroWpZRqKSbSS2JMBCWVnSykReRJESkWkRUtjp8qImtEZL2I3B7ApX4OvGxPlUop1XEZidEUVwZ/rHRE0K/4XU8D/wSebT4gIl7gX8D3gG3AQhF5C/ACd7X4+quB4cBKIMbmWpVSqt0yE6NtaUnbGtLGmLki0qvF4XHAemPMRgARmQGcZYy5CzioO0NEjgPigcHAfhGZZYw5aMS4iFwHXAfQo0ePIL4LpZQ6vIzEGJZvKw/6de1uSfuTCxQe8Pk2YHxrLzbG/BJARK4ESv0FtO91jwKPAowZM8YEq1illApERkI0xZ2tJR1Mxpinna5BKaVak5kUzb66RqprG4iPDl60OjG6YzuQf8Dneb5jHaYb0SqlnJKR4BuGF+TWtBMhvRDoJyK9RSQKmAq8FYwL60a0SimnNI+VDnaXh91D8F4EvgQGiMg2EZlujGkAbgbeA1YBLxtjvrGzDqWUsltmkj0tabtHd0xr5fgsYFaw7yciU4ApBQUFwb60UkodUvekWC4Z34OclOCOFu4UMw4Dpd0dSimnJMdFcuc5QxnZo1tQr+uqkFZKKbdxVUjr6A6llNu4KqS1u0Mp5TauCmmllHIbDWmllApjrgpp7ZNWSrmNq0Ja+6SVUm7jqpBWSim30ZBWSqkwpiGtlFJhzFUhrQ8OlVJu46qQ1geHSim3EWPct9OUiJQAW5yuwycdKHW6CId01ffeVd836Htv73svNcac6u+EK0M6nIjIImPMGKfrcEJXfe9d9X2Dvnc73rurujuUUsptNKSVUiqMaUjb71GnC3BQV33vXfV9g773oNM+aaWUCmPaklZKqTCmIa2UUmFMQzoIRORUEVkjIutF5HY/56NF5CXf+fki0iv0VdojgPd+pYiUiMhS38c1TtRpBxF5UkSKRWRFK+dFRP7h+7P5WkRGhbpGOwTwvo8Tkb0HfM9/Heoa7SIi+SLykYisFJFvROSHfl4T3O+7MUY/OvABeIENQB8gClgGDG7xmpuAh32/nwq85HTdIXzvVwL/dLpWm97/McAoYEUr508HZgMCTADmO11ziN73ccBMp+u06b13B0b5fp8IrPXzdz6o33dtSXfcOGC9MWajMaYOmAGc1eI1ZwHP+H7/KnCiiEgIa7RLIO/dtYwxc4Hdh3jJWcCzxjIPSBGR7qGpzj4BvG/XMsYUGWMW+35fCawCclu8LKjfdw3pjssFCg/4fBsHf9P+9xpjTAOwF0gLSXX2CuS9A5zn+2/fqyKSH5rSwkKgfz5udKSILBOR2SIyxOli7ODrthwJzG9xKqjfdw1pZbe3gV7GmGHAHL79H4Vyr8VAT2PMcOAB4A2H6wk6EUkA/gP8yBhTYee9NKQ7bjtwYOswz3fM72tEJAJIBspCUp29DvvejTFlxpha36ePA6NDVFs4COTvhusYYyqMMVW+388CIkUk3eGygkZEIrEC+gVjzGt+XhLU77uGdMctBPqJSG8RicJ6MPhWi9e8BVzh+/35wIfG94Shkzvse2/RF3cmVh9eV/EWcLnvaf8EYK8xpsjpouwmItnNz1xEZBxWzrihUYLvfT0BrDLG3NvKy4L6fY9o7xcqizGmQURuBt7DGu3wpDHmGxH5PbDIGPMW1jf1ORFZj/XAZapzFQdPgO/9FhE5E2jAeu9XOlZwkInIi1gjGdJFZBvwGyASwBjzMDAL60n/emAfcJUzlQZXAO/7fOBGEWkA9gNTXdIoAZgIXAYsF5GlvmO/AHqAPd93nRaulFJhTLs7lFIqjGlIK6VUGNOQVkqpMKYhrZRSYUxDWimlwpiGtHINEalyuoZAiMhvReSnTtehOgcNaaWUCmMa0sp1fDO9/ioiK0RkuYhc5DvuEZEHRWS1iMwRkVkicr7v3N2+NYK/FpG/+Y5N8a3/vURE3heRLN/x34rIMyLyqYhsEZFzReQvvnu965s2jIhsPuD4AhEp8FNrX9/XfOW73sDQ/UmpzkBDWrnRucAIYDhwEvBX3/T0c4FewGCsWWNHAohIGnAOMMS3ENQffdf5DJhgjBmJtQzrzw64R1/gBKyp7s8DHxljhmLNsDvjgNft9R3/J3Cfn1ofBX5gjBkN/BR4sEPvXLmOTgtXbnQ08KIxphHYJSKfAGN9x18xxjQBO0XkI9/r9wI1wBMiMhOY6TueB7zkC/goYNMB95htjKkXkeVYU+Lf9R1fjvUPQbMXD/j17wcW6VtJ7SjglQOWF49u97tWrqQtadXl+db4Hoe1IcNkvg3cB7B2lRkKXA/EHPBltb6vbQLqD1iboonvNn5MK78H6+ev3Bgz4oCPQcF4T8o9NKSVG30KXCQiXhHJwNruaQHwOdYGBB5f//Jx8L8WbbJvWc1bsbpJwFpStnmJySton4sO+PXLA0/41iHeJCIX+OoQERmOUgfQ7g7lRq9j9Tcvw2q9/swYs1NE/gOcCKzE2jljMVZXRyLwpojEYO1L92PfdX6L1RWxB/gQ6N2OWrqJyNdYLe9pfs5fAjwkIndgrSQ3w1e3UoCugqe6GBFJMMZU+R4WLgAmGmN22nSvzcAYY0ypHddXXYO2pFVXM1NEUrAeBP7BroBWKli0Ja2UUmFMHxwqpVQY05BWSqkwpiGtlFJhTENaKaXCmIa0UkqFsf8HWCk0lo+FajgAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"# inverse transform sampling"
],
"metadata": {
"id": "iTEWOT3UglAj"
}
},
{
"cell_type": "markdown",
"source": [
"### cumulative density function"
],
"metadata": {
"id": "V5-fdcZ8gz5B"
}
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from inverse transform sampling\n",
" data = pd.DataFrame.from_records([{\n",
" 'sample' : pareto_inverse_transform_sample(alpha=alpha),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='sample', kind='ecdf')\n",
"\n",
" # expected\n",
" x = np.geomspace(data['sample'].min(), data['sample'].max(), 100)\n",
" plt.gca().plot(x, stats.pareto.cdf(x, alpha),'r-', lw=5, alpha=0.6)\n",
"\n",
" plt.gca().set(xscale=\"log\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 390
},
"id": "e0xpMiYAgo-T",
"outputId": "d22e2c5a-d684-42ee-d590-9c8dfd26334d"
},
"execution_count": null,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"[None]"
]
},
"metadata": {},
"execution_count": 11
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"### probability density function"
],
"metadata": {
"id": "4yWIPzt9g5Jk"
}
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from inverse transform sampling\n",
" data = pd.DataFrame.from_records([{\n",
" 'logsample' : np.log( pareto_inverse_transform_sample(alpha=alpha) ),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='logsample', kind='kde')\n",
"\n",
" # expected\n",
" x = np.linspace(data['logsample'].min(), data['logsample'].max(), 100)\n",
" plt.gca().plot(x, stats.pareto.pdf(x, 1.0), 'r-', lw=5, alpha=0.6, label='pareto cdf')\n",
"\n",
" plt.gca().set(yscale=\"log\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "71FhGCw6g8Al",
"outputId": "3ee4c85e-5058-4832-8beb-f8b066be7ed4"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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hjQh3evRKOU6D8TBsLa0nKSacCeNx8W4oROCUU+Ckk+DFF4l87jlmTfAwMzuByoY2SmpaqGpsY2dZPd2l9fDeb2j86f3sW3g63tOWsmzGBJZPyyA6Qsvi1PijwXgYtpTWMXtC4tjv1Ga3iAg4/3w47TR45hlk3ToyE6LITLD+EevsNtS1tFPb3EFdSwdFm17mwHuv83958/j2pDlcuKiQ686YxMRUbdmpxo+QCsZ2bvro6OpmV3kjn1tWEPB7h6yEBFi9Gj72MXjySdiwAYwhzCOkxkaSGht57K3dxnB+wy52fbiDv+yZzKo35/Dps2Zw04qpxEWG1P+bKtUvXcAbov1Hmmjv6mZ6dgg2B7JbRobVxP7734f58/t9i0eErIQozsiJ4TexJdyz9RGq7n2A1bc+yXu+LnlKhTKdcgzRjvIGAKZlaiXFiOXkwJe+BMXF8NRTsGlTv2+LjvCyJD+RyQ2VvPXCH/jH+pcpvebTrLrkDCsvrVQICqmZsZ12ltfj9QiTMzSPOWp5efDlL8P3vmd1hxsgwGbER3LerCyWtxym4Sc/5a3Pfw3z1ltaFqdCks6Mh2hneQOT0mKJDNOV/oDJy4Prr4eyMnjhBfjXv6C7+yNviQzzcObUdN7ZX83+93cQd+udzJ2eYy0OnnEGpI7B07mV6ocG4yHaUd7A/Lwkp4cRmrKz4eqrrY5vL70Er7/+kZ16HhFOLUzBA2w5XEdEmIfpjc/B88/D7NlWUJ492+qdodQYpcF4CBrbOimpaeHyRXlODyW0paTApz8NF1xgBeSXX4Zaq0ueiLCoMIW2rm42HqohPjKMnORoq/fF5s2QnGzNlpcts/6s1BijU4kh2OlfvMvSxbugiImxusPddhtccw0UFgLWDHnJpFSSY8J5c+8RGlo7ez5TU2MtCn7723DnnfDee9DZOcADlHKfkJoZ21VnvKfSCsZTM7XrWFB5vbB4sfXavx9eeYXwDRs4fUo6z24u4629R1gxMxNP7wVAY2DrVusVG2t9dskSyM/XSgzlaiEVjI0xTwFPLVy48NpA3ndvVRMRYR5yk2MCeVs1HIWF1uvSS4l7803mh61l/YY9bD5cx7zcAXL5TU1Wx7hXXrHy0kuWWMFZ0xjKhUIqGNtlX1UjhamxoX0A6ViRkADnnceUc8/lyV89xvYXXiaroZnM+MgTf66sDB57DB5/HKZMsXponHyylRJRygU0GA/B3qomZujOO3fxePjijZ/kgu5U1jfW8/jJHqLfeRuOHj3x54yBXbus14MPWlUYixbB3LkQOUhAV8pGGowH0d7ZzaHqZi6Yk23fQ4yx794hLDYyjF98eh6fvudtftKdz623Xgg7d8Jbb8HGjYNvDunqsnYBbtoE4eEwZw4sWGB91cCsgkyD8SAOVTfR1W10551LLSxI4Zplhfz+jf2cPyebZdOnw/TpVoOi996zAvPevYPfqKPDCuAbN/YE5pNPtr5GactUZT8NxoPYW9UEwKQ0raRwq6+fO42Xd1TyzUc/5PmbzrC6vEVHW3XHp50GR45Yu/veeQcqKwe/Ye/AHBYGM2ZYPZrnzoV4TVcpe2gwHsTeqkYAJqXrzNitosK9/PzTc7n0d29z29rt3PapOR99Q1qadSDqBRfAwYPw7ruwfj3U1w9+887Ono0lIlBUZJ16PW+e1Y1OqQDRYDyIfVVNZMRHEh+lRwO52YKJKXzhtELufX0/58/O5rQpace/ScQ6HqqgAC69FHbvtnosb9wIjY2DP8QY6zO7d8Ojj0JWlhWU586FSZN0O7YalTERjEXkk8AFQAJwnzHmhWA9e29VI5PTNUUxFtx8zjRe2lHJt/7+Ic999fQT/wPq8cC0adbr8sut6ooNG+D996365KEoL7dezz9vlcjNnm29Zs2yDmpVahhs/6dcRO4XkUoR2dLn+koR2Skie0TklhPdwxjzhDHmWuCLwGfsHG+f57KvqkkX78aIqHAvP790HmV1Ldy2dsfQP+j1Wnnhq66CX/wCbrrJaj6UMIzt783NVvrj/vvh61+Hn/4Unn4aDhzQahk1JMGYGT8A3AX8yX9BRLzA3cAKoARYLyJPAl7g9j6f/7wxxr/q8j3f54LiaFM7dS0dung3hiyYmMy1p0/innX7WFSQzMUn5w7vBh6PVY0xfTpccQXs2wcffGDNmKuqhnYPY6zt2/v3W/0y4uKsYD9rlvU1Sbv/qePZHoyNMetEpKDP5cXAHmPMPgAR+StwkTHmduDCvvcQ6wTQnwLPGmM29vccEbkOuA4gPz8/IGPf56ukmJyhwXgs+fq509hUUsstf99MVmIUSyf3kz8eChGYPNl6XXyxtYvPX5c8nBlvY6O1YLh+vfX9hAkwc6YVmKdM0ZpmBTiXM84Bint9XwKccoL3fwX4OJAoIkXGmN/1fYMxZg2wBmDhwoUB+d+Fxyop0jRNMZaEez387soFXHbP23zuD+v53ZULWD59lJUPIlYQnTABzjvPqsTYvBk+/BC2b/9I/+VBlZZarxdftFIkkyb1zMYLCqxyOjXujInfujHmTuDOwd4X6K5teysbiQzzkJMUHZD7qeBJiongoWtP5ar73uXzf1zPjcuLuGF5EVHhATqpJSHB6p28bJlV/rZrF2zZYgXoodQy+3V19VRoPPWUNUsuKupZXMzP1yqNccKpYHwY6N2pPdd3bVQC3bVt35EmCtNi8WiDoDEpNS6SR7+0hO8/sZX/eXkPf3+vhK+dM41PnZQT2KZPYWFW2mHmTLjsMisY+9t47tgxvDP72tp6PgvW7j9/cJ46VYNzCHMqGK8HpohIIVYQvhy4YrQ3DfjMuKqR2TmJAbmXckZMRBi/vGwel5ycw+3P7uDrj2xizbq9fOXsKZw/J9ueTnwZGdZr+XIrEO/ZA9u2Wa+SkuHdq7XVmnFv8RUjRUZaOewpU6xXQYG1fVuNeWJsLrsRkYeAs4A0oAL4gTHmPhE5H/g1VgXF/caYWwP1zIULF5oNGzaM6h7tnd1M//6z3Li8iK+dMy1AIxvAbbdZO8N6+/a3rf/QVMB0dxue2VzGb17azZ7KRooy4vj2edP52IzM4A2ivt7KMe/YYQVn37FSIxYWBhMnWoG5qMgK1NoW1M0G/Nc/GNUUqwe4vhZYa/fzR+pwbQvdBiam6uJdqPB4hFXzJnD+nGzWbi7j1y/u4po/bmDlrCx+8ImZZCcGYW0gIcHqpXzKKVY1RmVlT3DeudOqVx6Ozk6rEVLvZkjZ2VZgnjTJ+pqerqecjAFjYgFvqAKZpjhUbf1HkZ+qs4xQ4/UF5XNnZfH7N/Zx50u7ef2XVdz6qTl88qSc4A1EBDIzrddZZ1nBuaTECso7d1qLgq2tw79vWZn1ev116/u4OCsw+18FBVpO50IhFYwDuYB3LBinaDAOVRFhHr58VhGr5k7g5oc38dW/fcDbe4/yw0/MIjoiQFUXwyECeXnW6+Mfh+5uKC62Ki127bK+DnfmDFad84cfWi//c3Jyeo6ymjTJ6rOhs2dHhVQwDqTi6mYiwzykx+kMItTlpcTw4LWn8KsXd/HbV/eyqaSWez+7kDyn/yH2eKx88MSJVnA2Bg4f7imF2717aJ3n+vLPwEtKembPUVHWcwoKrABdUGDtFNQAHTQhFYwDmqY42kxeSoyWtY0TYV4P3zh3OosKUvjKQ+/zqd++yT1XLWDBxBSnh9ZDBHJzrdfy5VZQraqy8sW7d1tfy8tHdu/W1p70iF9CghWU/UF64kTt52yjkArGgU5TaIpi/DlrWgaPf3kZ1/xxPavXvMPPLp0b3DzycIj0lNEtWWJda2y0gvK+fdbXAweGV+fcW339R9MbYJ2snZ9vBef8fOs1nIZKakAhFYwDxRhDcXUziwtdNCtSQVOUEccTX17GF//yHl/92wfsq2rkphVTkbHwP9nj4nqa34NVbVFSYjUt8gfpwQ5tPZGaGuu1aVPPtaSknsCcn2/lvJOTNcUxTCEVjAOVpqht7qChrdP5nKFyTHJsBH++5hS+98Rm7nx5D83tXXz3ghljIyD3FhbW01B/+XLrWkODFZT9neUOHBhZ1YZfba316j2Djo3tWYz0v7KydPfgCYRUMA5UmkIrKRRY1Rb/fclcYiLC+P0b++kyhv+8cObYC8h9xcd/dPZsjJVr3r/f2nx04IA1m+7sHPkzmpqs2ukdvfpKh4VZjZb8ee+8PKuqI1Zr+SHEgnGg+INxXoo2CBrvRIQfrJqJR4T739xPuNfDd86f4fSwAkvE2iiSnQ1Ll1rXOjutyg1/cD540Oo019098ud0dsKhQ9art+RkKyj7g3ROjlV77XWgvNBBGoz7cSwYJ+vMWFkB+fsXzqCzu5s16/aRnxLDladOdHpY9vJvs5440Tr1BKyFwOJiK5gePGh9HW2Ahp489JZehwF5vVZaIyfHmk3n5FivlJSQzUWHVDAOVM64uLqZtLgIYiND6v88ahSsGfIsSmpa+OGTW5mRncCCiclODyu4wsN7dvH5dXRYM2h/kD50yPp+pBUcfl1d1n0O92nmGBnZ01d6wgRrNj9hQkjURIdUtAlkzlgX71RfXo/w68vnc+Gdb3DjgxtZ+++nkxwb4fSwnBUe3rNA6NfdbeWgi4ut3LM/UA/1oNcTaWvrWXjsLSrqo8E5O9uaWY+hmXRIBeNAOVTdPP5mPWpIEqLCufuKk/nUb9/kx89s447L5js9JPfxeHpmrqf4DvAxBurqeoJzSYk16y0vD8yBra2tVoXIvn0fvR4ZaQXlrKyevHh2tlWb7bIgrcG4j46ubsrqWrWSQg1oTm4iXzprMv/z8h4+OT+HM6amOz0k9xOxUglJSTB7ds/1jg4r7+xPSfhfI9nm3Z+2Niu/3btFbUwM3HFHYO4fQBqM+yirbaWr22iaQp3QDcuLeGZzGd95fDMv3HQGMRH6n9KIhIf3LBT21tDQE5j9wbq0dHhnDQ4kO9t1s2IIsWAciAU8rTFWQxEV7uWnF8/lsnve5o4XdvG9C2c6PaTQEh/fc0irnzFQXd1zoGtpqdUqtLR0eAuG2dmBH28AhFQwDsQCngZjNVSLC1O44pR87n9zP5csyGVGtvZosJUIpKZarzlzeq4bY23xLi21ctD+IF1W1v9MWoPx2HCoupkIr4fMhCinh6LGgG+eO421m8v40VPbePDaU8b+7ryxSATS0qzX3Lk9142xtmn7A3N5ufU1L2/gezlIg3EfxdXN5CZH23NQpQo5STER3LxiKt//x1ae31rOytnunHWNSyLW7r7kZOvkbpfTrh19lNQ0k5Os26DV0K1enM+0zHh+8sx2Wju6nB6OGqM0GPdxuLaVnCQNxmrowrwe/nPVTEpqWrjvjf2Df0Cpfmgw7qWts4sjjW3BOSVYhZRlRWmcOyuTu1/ZQ3ndKNpRqnFLg3Ev/v+IJiTp4p0avu+eP5POLsPPntsx+JuV6iOkgrGIrBKRNXV1dSP6fGmtFYw1TaFGIj81hi+cXshj7x/mrb1HnB6OGmNCKhgbY54yxlyXmJg4os+X1rYAkK3BWI3QV86eQkFqDN9+bDMt7bqYp4YupILxaB0LxomaplAjEx3h5aeXzOXg0WZ+9PRWp4ejxhCtM+6ltK6VtLgIosLH1wkDKrBOnZTKl8+azG9f3ctJ+clcttCdmwwAjjS28cCbB9h/tIm02AiuWlJAUUac08MalzQY91Ja26KVFCogvrZiKptKavnOY5tJig7nnFlZTg/pOM98WMY3Ht1EW2c3E1NjOFzTwp/+dZDbPjWH1YvznR7euKNpil5Ka1u0kkIFRJjXwz1XLWR2TiI3PLiRP//rICYQfXsD5OENxdz40EZmZCfwz5vO4OWbz+KtW87mzKnpfPuxzTz+fonTQxx3NBj7GGN8wVhnxiow4iLD+OPnF3NaURrff2ILn39gPXsqG5weFu8drOY7j23mtKI0/nLNKUxKt9ISqXGR3HPVAhYXpvCfT2zVeukg02DsU9/aSVN7FxM0TaECKDE6nPuuXsT3LpjB+gM1fPyOdVx13zu8uK2Cru7gz5Qr61v50l82kpMczV1XnEx0xEfXRyLDvPz80rl0dHfz/X9sGeAuyg4ajH38lRQ6M1aB5vEIXzh9EgHi+vEAACAASURBVK9+4yxuXjGV3RWNfOFPG1j+i1e5/439NLSO8vDOIero6uaGBzfS0NrJPVctIDE6vN/3TUyN5StnT+Gf2yr4sKQ2KGNTYyAYi8gMEfmdiDwqIl+y6zlldf5grDljZY+0uEi+8rEpvP6t5dx9xclkxEfyo6e3sfT2l1mzbi/tnaM88n4Qtz6znfUHavjpJXOYnnXi3stXLy0gISqM376y19YxqR62BmMRuV9EKkVkS5/rK0Vkp4jsEZFbTnQPY8x2Y8wXgcuAZXaN9XCtfyu0zoyVvcK9Hi6Ym82jX1rKP25YxqLCFG5bu4OL7n6TXRX25JQf21jCA28d4JrTCrlofs6g74+LDOPqpQU8v62cvVWNtoxJfZTdM+MHgJW9L4iIF7gbOA+YCawWkZkiMkdEnu7zyvB95hPAM8BauwZaVttCuFdIj4u06xFKHWdeXhL3/79F3PvZhVTWt3LRXW/y7OaygD7jlR2VfPPRDzl1Ugq3nDd98A/4fHZJAV4RHt5QHNDxqP7ZGoyNMeuA6j6XFwN7jDH7jDHtwF+Bi4wxm40xF/Z5Vfru86Qx5jzg3+waa2ltC1mJUXi0qbxywIqZmTz7H6czPTueL/3fRn71z110j3KBzxjDA2/u5/o/v8eM7ATWfHYh4d6h/yefHh/JWdPSeeL9w44sNo43Q9r0ISKPAfcBzxpjRpvYygF6/1NbApxygmefBVwMRHKCmbGIXAdcB5CfP/yC9dLaVt3woRyVkRDFQ9eeynce38xvXtrNrooGfnnZvEFPnm5u72RXRSOltS0cbWqnurGdo01trNtVxYGjzZw9PYNffnoeCVH9L9idyCUn5/Li9kre2HOEM6emj/RHU0Mw1B14vwU+B9wpIo8AfzDG7LRvWD2MMa8Crw7hfWtEpAxYFRERsWC4zymta2FRQcrwB6hUAEWFe/nlp+cxMzuB29ZuZ9/dTfz803OZm5v0kfc1tHbwz20VPLWplNd3H6Gzz8w1ISqMmRMSuGnFVD4xb8KIz+Y7e0YGidHhPPH+YQ3GNhtSMDbGvAi8KCKJwGrfn4uBe4G/GGOGU5tzGOi9WT/Xd23URno6dFe3obyuVRsEKVcQsUrhpmTG881HN/HJu9/kjKnpLC5MwRj4oLiW13ZV0d7ZTU5SNJ8/rZAFE5PJT4khNTaC5NiIYaUjTiQyzMvHZ2Ty4vYKOru6CQvQfdXxhtybQkRSgSuBq4D3gf8DTgOuBs4axjPXA1NEpBArCF8OXDGMzwdcVUMbnd1GKymUq5w5NZ0XbjqT37++j0ffK+HVnVUA5KVEc8XifFbNm8DJ+Um2n0i9YmYGf99YwvoDNSyZnGrrs+xw6Ggzj75XTEtHF8unZbC0KM3pIfVrqDnjx4FpwJ+BVcYY/3Lv30Rkwwk+9xBWoE4TkRLgB8aY+0TkRuB5wAvcb4wJSK9BEVkFrCoqKhrW50p9NcbaVF65TWJ0ODefM42bz5lGS3sXXcYQFxnc/l6nT0knIszDi9srxlwwfujdQ/zwya10dHUT5vFw7+v7+cS8Cdxx2TzXzfKH+lu91xjzkcUzEYk0xrQZYxYO9CFjzOoBrq/FhjK1kaYpeprKa5pCuVffrcvBEhsZxrLJqfxzWwXfu2CG7TPxQHlpewXfedzqwfGzS+eSHBPB/766l9+8tJvYyDBu+9RsV/0sQ/2n4Sf9XHs7kAMJhJEeu1SmGz6UOqHl0zM4VN1McXWL00MZksqGVv7jrx8we0Iia65aSHZiNFHhXm5aMZUvnzWZh949xDMBrucerRMGYxHJEpEFQLSInCQiJ/teZwExQRnhMIz02KVrTitk/Xc/PqLSH6XGg6WTrTzrm2PkbL87XthFW2cXd64+6bj/RXHzOdOYkZ3A7Wt3uOporMFmxucCv8CqeLgD+KXv9TXgO/YOLXg8HiE9XnfeKTWQyemxZMRH8tbeo04PZVA7yuv524ZiPrukgMK02OP+3usRfrBqJodrW7j/zf0OjLB/J8wZG2P+CPxRRC4xxvw9SGMasZEu4CmlTkxEWFaUxuu7qzDGuCrX2te96/YTHe7lK2cPHAdOnZTKGVPTeeCtA1x7+iQiwpxfzBssTXGl748FIvK1vq8gjG9YRns6tFJqYEsmp3KksZ1dFe5tHHS0sY2nPizl4pNzSIqJOOF7P7esgKqGNp7d4o7c8WD/HPjn+HFAfD8vpdQ4sWSSVdb2zn73pir+tqGY9s5url5SMOh7z5ySzqS0WP7w5gHbxzUUg6Up7vF9/a/gDGd0NE2hlH1yk6PJiI9k48EaPjuEYBdsxhge3VDCKYUpTMkcfK7o8QhXnJLPT57Zzv4jTf3ml4NpSIkSEfmZiCSISLiIvCQiVb1SGK6haQql7CMiLJiYzHuHapweSr+2ldWz70jTkPo1+104dwIi8NSmUhtHNjRDzVqfY4ypBy4EDgBFwDfsGpRSyp0WTEymuLqFygb3HVb6zIdleD3CytlZQ/5MVmIUiwpSeHJTqeOndw81GPvTGRcAjxhjhrerQikVEk7KTwZg40F3nY1njOHpD8tYOjmVlNgTL9z1tWreBPZUNrKj3NmTu4cajJ8WkR3AAuAlEUkHXPdP40h34CmlhmZ2TgIRXg8bXZaq2FnRwKHqZs6fkz3sz547KxOAl3dUBnpYwzKkYGyMuQVYCiz0tctsAi6yc2AjoTljpewVGeZlVk4CHxxy18z4NV9Hu+XTMob92Yz4KGZNSODVnWMgGPtMBz4jIp8FLgXOsWdISik3m5OTyNbSulEfCxVIr+2qYnpWPFkj7Em+fFoGGw/VUtcynNbsgTXUaoo/Y22LPg1Y5HsN2K1NKRW6Zuck0tTexb4jTU4PBYCmtk7WH6ge1UkkZ01Lp6vb8MZu53pvDLWF5kJgpnF6uVEp5bg5OVYacMvhOooy4hweDby99ygdXYYzp408GM/PSyIxOpzXdlVywdzh550DYahpii3A0OtFlFIha0pGHJFhHjYfdsdC+Vt7jxIV7mHBxOQR3yPM62FxYQrv7O97mH3wDHVmnAZsE5F3gTb/RWPMJ2wZ1QjpDjyl7Bfm9TAjO8E1wfjdA0c5OT+ZyLDRNd8/pTCFf26roLyudcS559EYajD+oZ2DCJSRnvShlBqeOTmJPLaxhO5ug8fjXAe3+tYOtpXW8+8fmzLqe53aq/fGcHbxBcpQS9tew9p5F+7783pgo43jUi5uUajUrAkJNLV3UVzT7Og43jtYQ7eBxYUpo77XjOwE4qPC+Nc+Z1IVQ62muBZ4FLjHdykHeMKuQSml3G16dgIA28uc3bX2zr5qwr3CSXkjzxf7eT3CooIUx7rSDXUB7wZgGVAPYIzZDQy/ulopFRKmZsYhAjsd3kK8/kA1c3ISA3ZY68KCZPZVNVHT1B6Q+w3HUINxmzHm2OhEJAzQMjelxqmYiDAmpsSwo7zesTF0dHWz5XAdJ+ePflbsNz8vCYAPSoK/w3Cowfg1EfkO1sGkK4BHgKfsG5ZSyu2mZyU4OjPeWd5AW2c383wBNBDm5iYhgiPbvYcajG8BqoDNwPXAWuB7dg1qpLRRkFLBMz07nv1Hmxw7YfmDYitgzg9gMI6LDGNqRvyxewfTUKspurEW7L5sjLnUGHOvG3fjaaMgpYJnelYCxsCuCmdmx5uKa0mNjSA3OTqg952fl8Smktqg9zce7EBSEZEfisgRYCew03fKx38GZ3hKKbeanmUdbeRUquKD4lrm5SUF/KTq+flJ1DZ3cPBocMv2BpsZ34RVRbHIGJNijEkBTgGWichNto9OKeVaeSkxRIR52FMV/NOiG1o72FPVGNAUhd+8XOuem4K8iDdYML4KWG2M2e+/YIzZB1wJfNbOgSml3M3rESalxbLbgTTF9rIGjOlpWhRIUzLjiPB62FYa3EqRwYJxuDHmuJ5yxpgqINyeISmlxoopmfGOzIy3lVqL9LMmJAT83uFeD1Oz4tjqsmB8osrn4FdFK6VcpSg9jpKalqBXVGwtrSctLoL0+Ehb7j8r22qgH8xFvMGC8TwRqe/n1QDMCcYAlVLuVZQRhzGwN8iz421l9czITgj44p3frJwEapo7KKsL3lGfJwzGxhivMSahn1e8MUbTFEqNc/7m8sEMxu2d3eyuaGSmDSkKP3/6I5h54+GcgecYEYkVkQ0icqHTY1FK9ShIi8HrEXZXBC8Y76lspL2rm1kT7NtPMD0rARGCmje2NRiLyP0iUikiW/pcXykiO0Vkj4jcMoRbfQt42J5RKqVGKjLMy8SUGHZXBq+iYluZFSBnZts3M46NDKMwNZZtZcHbzTvU5vIj9QBwF/An/wUR8QJ3AyuAEmC9iDwJeIHb+3z+88A8YBsQ/Nb7SqlBTUqPY38QDyfdUVZPZJiHwrRYW58zLSs+qBtabA3Gxph1IlLQ5/JiYI+vXhkR+StwkTHmduC4NISInAXEAjOBFhFZ69uerZRygUnpsazbXRW0Uz92VTZSlBGH1+ZnTc2M5/mt5bR2dBEVHpgWnSfiRM44Byju9X2J71q/jDHfNcZ8FXgQuHegQCwi1/nyyhuqqqoCOmCl1MAKUmNp7+ymtK4lKM/bVd7AtMx4258zLSuebmPlqINhTCzgARhjHjDGPH2Cv19jjFlojFmYnj7yI7uVUsPjTxcEI1VR19JBeX0rU7PsD8ZTfQE/WI2QnAjGh4G8Xt/n+q6NmrbQVCr4JqUHLxj7t15PzYyz/VkFqTFEeD3sDOFgvB6YIiKFIhIBXA48GYgbawtNpYIvIz6SmAgv+6rsD8a7fCV0U4OQpgjzepicEceuIC3i2V3a9hDwNjBNREpE5BpjTCdwI/A8sB142BizNUDP05mxUkEmIhSmxQZlZryrooHYCC85SYHtYTyQqZlxx/4BsJutwdgYs9oYk22MCTfG5Bpj7vNdX2uMmWqMmWyMuTWAz9OZsVIOCFYw3lnewJTMeNu2Qfc1NTOew7UtNLZ12v6sMbOANxQ6M1bKGYVpsZTUNNPWaW/DoH1HGo9twQ6GyenWs/YFYbt3SAVjnRkr5YyJqbF0GzhcY195W1NbJxX1bbZv9uitKMN6VjDy4SEVjJVSzshPiQGg2MZg7E+DTApiMM5PicXrkaA0QgqpYKxpCqWckZdiLagVV9t3bpw/GBemBy8YR4R5mJgSo8F4uDRNoZQzMuOjiPB6ghKMC1KDF4zB6r2xt1LTFEqpMcDjEXKToymusTcY5yRFB6VPRG+TM6xKka5ue0/9CKlgrGkKpZyTlxLDIRtnxvuONFGQFmPb/QcyOS2O9q5uSmz8hwZCLBhrmkIp5+SlRFNcbc8CnjGG/VWNQa2k8Jvsq6iwO28cUsFYKeWc/JQY6lo6qGvpCPi9a5o7qG/tpDAteDXGfv5n7j+iM2Ol1BiQl+wrb7MhVbH/iDUrDWZZm19yTDgJUWEcsHmHoQZjpVRA5KXYF4z9my6cSFOICAVpsRw4qsF4yHQBTynnHAvGNix07T/SRJivYsMJBakajIdFF/CUck5idDiJ0eG2VFTsP9JEfkoMYV5nQlZBagyHa1po77TvxLeQCsZKKWfZVVGx/0iTIykKv4I0q/eGnXXUGoyVUgGTlxwT8IDV3W0cD8YTfbv+7FzE02CslAqY/JQYSqpb6A7gbrXy+lbaOruD2pOiL/8/BAeO6sx4SHQBTyln5abE0N7VTWVDW8DueaxBkIMz4+SYcOJtLm8LqWCsC3hKOcvfSjOQi3j7XBCMRcT2ioqQCsZKKWflJQe+lebBI01EhXvIjI8K2D1HIi8l2tbm+RqMlVIBk5McjUhgZ8YlNS3kJsfg8QTn3LuB5CXHUFIT2Hx4bxqMlVIBExnmJSshKqAVFcU1zY5t9ugtNzma9q5uqhoDlw/vTYOxUiqg8pJjApqmsGbGLgjGNm73Bg3GSqkAm5AURWlta0DuVd9qdYHLTQ5+H+O+/PnwEpvyxiEVjLW0TSnnZSdFU1HfGpCTMUp8u/nyXBCMc23sSgchFoy1tE0p501IjKKz23AkALlV/+kabkhTRIV7SYuL1JmxUmpsmJBkBc7S2tEHLX/gc0MwBl/vDZv6U2gwVkoFVHaiFTjL6kafNy6paSEmwktKbMSo7xUIub7yNjtoMFZKBdSEJGtzRiBmxv6yNhFna4z98pKjKa1tseWkaA3GSqmASowOJzrcG7CZsRsqKfxyk2Po7DaU1wemWqQ3DcZKqYASEbKToiirC0TO2B0bPvzyUgK/3dtPg7FSKuAmJEaPuta4rrmDhtZOV5S1+fln6XbkjTUYK6UCLjtx9DPjYheVtflNSIpCRGfGSqkxIjspmsqGNjq6Rn5mXE9Zm3tmxpFhXjLjo8bnzFhEzhKR10XkdyJyltPjUUoNbkJiFMZAxSgWuty04aM3u2qNbQ3GInK/iFSKyJY+11eKyE4R2SMitwxyGwM0AlFAiV1jVUoFTnbS6GuNS2paiIsMIykmPFDDCojc5Bhb+hrbPTN+AFjZ+4KIeIG7gfOAmcBqEZkpInNE5Ok+rwzgdWPMecC3gP+yebxKqQCYkDj6WuMSl9UY++UlR1NW1zKqFEx/wgJ6tz6MMetEpKDP5cXAHmPMPgAR+StwkTHmduDCE9yuBogc6C9F5DrgOoD8/PxRjFopNVrZx7ZEj25m7LYUBVgz424DZbWt5KcGLp/tRM44Byju9X2J71q/RORiEbkH+DNw10DvM8asMcYsNMYsTE9PD9hglVLDFxcZRnxU2IgrKowxFFc3u2rxzi/XX2sc4LyxrTPjQDDGPAY8NpT3isgqYFVRUZG9g1JKDWo0tca1zR00tXe5cmacd6zWOLDB2ImZ8WEgr9f3ub5ro6YtNJVyj9HswnNbt7beshOj+Nmlczl1UmpA7+tEMF4PTBGRQhGJAC4HngzEjbW5vFLukZ0YPeJqCn8Q97fjdJMwr4fLFuYxMTU2oPe1u7TtIeBtYJqIlIjINcaYTuBG4HlgO/CwMWZrIJ6nM2Ol3GNCYhTVTe20dnQN+7P+RjxZvqqM8cDuaorVA1xfC6y189lKKWf1rjUuTBveLLK0tpVwr5AWO2ABVchx/Q684dA0hVLu4a81LhtBrXF5XQuZCVF4PO6qMbZTSAVjTVMo5R7Hao1HkDcuq2slexylKCDEgrHOjJVyj+zRzIzrW8lKdN/inZ1CKhjrzFgp94gK95IYHU5lw/BOiTbG6MxYKaUCKTMhksqG4aUpapo7aO/sJitBg7EKNhP4ww2VcoPMhCgq6oc3M/bXGOvMeAzTnLFS7pIeH0nlMHsal/sW/LJduOHDTiEVjDVnrJS7ZCZEUdnQRvcwjrb379rTmbFSSgVIZnwknd2Gmub2IX+mrK4Fr0dIixs/Gz5Ag7FSykYZvkW44eSNy+payYyPxDuONnxAiAVjzRkr5S6ZCdbstmIYFRXlda3jqieFX0gFY80ZK+UuGfFWUK0axsy4vK6V7HG24QNCLBgrpdwlPd43Mx5iRYV/w4fOjJVSKoCiwr0kxYQPOU1R39JJS0fXuKukAA3GSimbZcYPfeNHWb1/w4emKcY0XcBTyn0yEiKH3J/CX2OsaYoxThfwlHKfjPioIe/CK6sdnxs+IMSCsVLKfTITIqka4i688roWPNKz8DeeaDBWStkqMyGKzm5D9RB24ZXVtZIeH0m4d/yFpvH3EyulgipjGOVt47GpvJ8GY6WUrfxboiuHUFFRVtdK9jjrY+ynwVgpZatjW6KHMDOuGKcbPiDEgrGWtinlPv7FuMHK25rbO2lo6yQjYfwt3kGIBWMtbVPKfSLDvCTHhA86M/anMTLjdWaslFK2GMrxS/5grTNjpZSySUZC1KAHk/rTGJm6gKeUUvbIiI8ctJri2Mx4HG74AA3GSqkgyEyIpKqxja4T7MKramgjIsxDYnR4EEfmHhqMlVK2y0yIoqvbcLRp4NlxRX0rGfGRiIyv45b8NBgrpWznTz2cKFVR2dA2bvPFoMFYKRUE6f7jl05Qa+yfGY9XGoyVUrY7NjM+QUXFeJ8Zhzk9gMGIiAf4MZAAbDDG/NHhISmlhil9kDRFS3sXDa2d47J1pp+tM2MRuV9EKkVkS5/rK0Vkp4jsEZFbBrnNRUAu0AGU2DVWpZR9osK9JESFUdXYfzD2z5h1ZmyfB4C7gD/5L4iIF7gbWIEVXNeLyJOAF7i9z+c/D0wD3jLG3CMijwIv2TxmpZQNMhKiBpwZ+3fnjeecsa3B2BizTkQK+lxeDOwxxuwDEJG/AhcZY24HLux7DxEpAfxdqbsGepaIXAdcB5Cfnz/qsSulAisjPnLAnLHOjJ1ZwMsBint9X+K7NpDHgHNF5H+AdQO9yRizxhiz0BizMD09PTAjVUoFTHr8wAeT6sx4DCzgGWOagWuG8l4RWQWsKioqsndQSqlhy4i3zsIzxhy3saOyoZUIr4ekmPG5+w6cmRkfBvJ6fZ/ruzZq2kJTKffKiI+irbOb+tbO4/6usr6N9HG8+w6cCcbrgSkiUigiEcDlwJOBuLE2l1fKvfytMav6yRtXNrQeOxFkvLK7tO0h4G1gmoiUiMg1xphO4EbgeWA78LAxZmsgnqczY6Xc60S1xhX1bWSM06byfnZXU6we4PpaYK2dz1ZKuYt/ca6/WuPK+laWTU4N9pBcJaS2Q2uaQin38ven6Dszbu3oor6189gp0uNVSAVjTVMo5V4JUWFEhnmOqzWu1LI2IMSCsVLKvUSEjITja40rGvxn3+nMOGRomkIpd0uPizyujeaxU6G1miJ0aJpCKXfLiI86fmZ87Ow7nRkrpVRQZCREUlnfJ2fc0Ea4V0gex7vvIMSCsaYplHK3jPhI6ls7ae3o6fllnfARNa5330GIBWNNUyjlbhn9HL9UVtdCduL4TlFAiAVjpZS7HduF1ysYl9e1kp0U7dSQXEODsVIqaPzB2N+fwhhDWV2rzowJsWCsOWOl3M3fLMg/M65p7qCts5uscV5jDCEWjDVnrJS7pcZG4pGenHFZXQuAzowJsWCslHI3r0dIjYs8ttGjrNZKV2jOWIOxUirIep+FV+arOdaZsQZjpVSQZfQ6C6+8roUwj5AWN763QkOIBWNdwFPK/XKTYzh0tNmqpKhtJTMhCq9nfG/4gBALxrqAp5T7Tc2Kp6Gtk9K6VsrqWsnSFAUQYsFYKeV+07PiAdhV3kB5vQZjPw3GSqmgmpphBeP3i2s5XNNCbrJWUoAGY6VUkCXGhJOdGMWD7xykvaubM6akOz0kV9BgrJQKuqmZ8RxpbCchKozFhSlOD8cVNBgrpYLOnzdePj2DcK+GIdBgrJRywNRMKxivmJnp8EjcI8zpAQSSiKwCVhUVFTk9FKXUCaycnUVlQ5sG415CamasdcZKjQ2xkWF86azJRIZ5nR6Ka4RUMFZKqbFKg7FSSrmABmOllHIBDcZKKeUCGoyVUsoFNBgrpZQLaDBWSikXcP2mDxE5Hfg3rLHONMYsdXhISikVcLbOjEXkfhGpFJEtfa6vFJGdIrJHRG450T2MMa8bY74IPA380c7xKqWUU+yeGT8A3AX8yX9BRLzA3cAKoARYLyJPAl7g9j6f/7wxptL35yuAa2wer1JKOcLWYGyMWSciBX0uLwb2GGP2AYjIX4GLjDG3Axf2dx8RyQfqjDENAz1LRK4DrgPIz88f/eCVUiqInFjAywGKe31f4rt2ItcAfzjRG4wxa4wxC40xC9PTtVm1Umpscf0CHoAx5gfDef977713REQO2jWeIUoDjoz402vWBG4kwTe6n33sG88//3j+2WHwn/85Y8zK/v7CiWB8GMjr9X2u71rAGGMcnxqLyAZjzEKnx+GE8fyzw/j++cfzzw6j+/mdSFOsB6aISKGIRACXA086MA6llHINu0vbHgLeBqaJSImIXGOM6QRuBJ4HtgMPG2O22jkOpZRyO7urKVYPcH0tsNbOZ7vAmE76jtJ4/tlhfP/84/lnh1H8/GKMCeRAlFJKjYD2plBKKRfQYKyUUi6gwTjAhtN3IxSJyAER2SwiH4jIBqfHY7f++q+ISIqI/FNEdvu+Jjs5RrsM8LP/UEQO+37/H4jI+U6O0S4ikicir4jINhHZKiL/4bs+4t+9BuMA6tV34zxgJrBaRGY6OypHLDfGzB8n9aYPAH2L+G8BXjLGTAFe8n0fih7g+J8d4Fe+3/9832J9KOoEbjbGzAROBW7w/bc+4t+9BuPAOtZ3wxjTDvwVuMjhMSkbGWPWAdV9Ll9ET4fBPwKfDOqggmSAn31cMMaUGWM2+v7cgFWmm8MofvcajANrJH03Qo0BXhCR93zNm8ajTGNMme/P5UCmk4NxwI0i8qEvjRGSKZrefM3QTgLeYRS/ew3GKtBOM8acjJWquUFEznB6QE4yVu3oeKof/V9gMjAfKAN+6exw7CUiccDfga8aY+p7/91wf/cajAPL9r4bbmeMOez7Wgk8jpW6GW8qRCQbwPe1cpD3hwxjTIUxpssY0w3cSwj//kUkHCsQ/58x5jHf5RH/7jUYB9a47rshIrEiEu//M3AOsOXEnwpJTwJX+/58NfAPB8cSVP5A5PMpQvT3LyIC3AdsN8bc0euvRvy71x14AeYr5fk11skl9xtjbnV4SEEjIpOwZsNgbbV/MNR/fl//lbOwWidWAD8AngAeBvKBg8BlxpiQW+ga4Gc/CytFYYADwPW9cqghQ0ROA14HNgPdvsvfwcobj+h3r8FYKaVcQNMUSinlAhqMlVLKBTQYK6WUC2gwVkopF9BgrJRSLqDBWI1pItLo9BiGwtfN7OtOj0O5lwZjpZRyAQ3GKiSI5ecissXXT/kzvuseEfmtiOzw9ZddKyKX+v7up75+tB+KyC9811aJyDsi8r6IvCgimb7rPxSRP4rI6yJyUEQuFpGf+Z71nG9rrL+fs//6uyJS1M9YJ/s+857vftOD938pfUFLEgAAAflJREFU5VYajFWouBhr59c84OPAz31bcy8GCrD6S18FLAEQkVSs7bqzjDFzgZ/47vMGcKox5iSsFqjf7PWMycDZwCeAvwCvGGPmAC3ABb3eV+e7fhfWbsy+1gBfMcYsAL4O/HZUP7kKCbaeDq1UEJ0GPGSM6cJq1vIasMh3/RFf45pyEXnF9/46oBW4T0SeBp72Xc8F/uYL5BHA/l7PeNYY0yEim7G2uz/nu74ZK+D7PdTr6696D9LX5Wsp8IjV3gCAyBH/1Cpk6MxYjUvGmE6sjmKPAhfSE1j/B7jLN7O9Hojq9bE232e7gQ7T00ugm49ObMwAfwbrv7naXidhzDfGzAjEz6TGNg3GKlS8DnxGRLwikg6cAbwLvAlc4ssdZ2I1svHPUBN9xwLdhJXeAEikp+3p1YzMZ3p9fbv3X/h63u4XkU/7xiEiMg817mmaQoWKx7HywZuwZqPfNMaUi8jfgY8B27BOYdmIlaKIB/4hIlGAAF/z3eeHWCmEGuBloHAEY0kWkQ+xZtKr+/n7fwP+V0S+B4Rj5aY3jeA5KoRo1zYV8kQkzhjT6Fu0exdYZowpt+lZB4CFxpgjdtxfhS6dGavx4GkRScJakPuxXYFYqdHQmbFSSrmALuAppZQLaDBWSikX0GCslFIuoMFYKaVcQIOxUkq5wP8HURzJJKeKAowAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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MzuefVx9HS7ubr93/Ce9v8GOVGx8PX/ua1Vs9eXLvn+d2w/vvW6WSl17S02BU2NAk7ac1e+opzU/Vm4Y+mjI8nZeum8mwjES+89jnPL5ou38XzM2F666zzlYsKOj981pbrcMFbrsNXn/d+lgpB9Mk7YdOt2H9vnotdQzQ0PQEnrvmOE4dl8NPX1rDL19dS+dAhzV5lJZaq+VLL4W+Bm01NcGLL1rJ+u23tW1POZbjk7SIjBSRR0TkObtj6W5b1UFa2t2U6k3DAUuKi+bBS8u47PhiHvloG9c+sZTmtgF0fhzJ5YITTrDq1eecY5VEetPQYB2Iq8laOVRQk7SIPCoilSKyutvzs0Vkg4hsFpFb+rqGMWarMeaKYMY5UGv2WDehSvM1SfsjyiXcfvYEfjavlLfXVXDRQ4uobBjAdvLu4uLgq1+1Drr9yles0ai9qa+3kvWtt8Jbb1kHDyjlAMFeST8GzD7yCRGJAu4DzgJKgfkiUioik0Tk1W6PnCDH55dNFQeJcgmjciLnuCw7XT5zBA9eWsbGioOcd98nA+/86C4lBS680FpZz5zZdydIQwP8619Wsn71VWvynlI2CmqSNsYsBLoPGp4BbO5aIbcBTwPnGGNWGWPmdnt4fdtfRK4SkSUismT/fj/O4fPBpsoGijMTiYuOCsn7DQanl+byzNXH0dbp5msPfMLHm6sCd/GMDPjWt6xOkGOO6f1EGLCS8yuvwI9+ZCXtAwcCF4dSPrCjJl0A7Dri4/Ku53okIpki8hdgqoj8qLfPM8Y8ZIwpM8aUZWdnBy7aPmyqOMjonJSQvNdgMmlYGi9eN5OhaQl8+9HPeGbJrv6/yBe5ufCd71i902VlfSfr1lar/HHrrfD447B3b2BjUaofjr9xaIypNsZcY4wZZYy5w+54PFraO9le3ciY3GS7Q4lIBekJPHvtcRw3KpMfPreSP7y5wb/Db3uSn28dMuA5FaavZN3ZCR9/bK3C77sPNm7U2SAqJOxI0ruB4Ud8PKzrOb+F8iDabVWNuA2U5OpKOlhS42N49LKjmT9jOPe+t5kbnv6ClnY/Oz96kp9vTdr7xS/g+OP7rlkDrFwJf/wj/OY3sHixHjyggsqOJP05MFpERohILHAR8HIgLhzKg2g9N7V0JR1cMVEufnPeJP5n9jheXrGHSx9ZTE1jkNrkcnLg29+GX/8aTjkFYmL6/vydO+HRR61SyIIF1k1HpQIs2C14TwGLgLEiUi4iVxhjOoDvAW8C64BnjDFrghlHMGyutDo7RmRpZ0ewiQjXzhrFvRdPZUV5Heff//HAZlN7KyMDLroI7rgD5syxzl/sS12dtdX8llvgb3+zkrdSASIBr/PZSETmAfNKSkqu3LRpU1Df6+q/L2FT5UHe/e9ZQX2fgLnuui//WH7ffX33DjvQ0h01XPn4UowxPPStMo4uzgj+m7a2WvXot9/2/vSXkSNh1iyYPj3svsfKFr3eEHH8jUNfhLLcsanyIKNztNQRatOLMnjhv45nSGIslzy8OPCdHz2Ji4NTT7U2xVx5JRQX9/81W7dapZBbboHnn4eqALYSqkFF/4kfgNaOTnZUNzFnUr7doQxKRZlJPP9fx/O9J5fzw+dWsmZ3HT+eW0pMVJDXHC6X1bI3fbqVhN9+G5Yv77vLo6EB3nzTauMrLYUTT7Sm9UVpb73yTkQl6SPKHUF9n21VjXS6DSW6krZNemIsj11+NHe+uYGHFm5l3d4G7rtkGtkpccF/cxEYNcp6VFfDBx/ARx/1vTvRGFizxnqkpVldJCecAFlZwY9XhTUtdwzAxoqDAIzR9jtbRUe5uPWr47n7oims3H2As+/9iKU7akMbRGamdaTXb39r7WYcNqz/r6mrs8ak3nYb/PnPVhtfe3vwY1VhKaJW0qGyuaIBl6CdHQ5xzpQCSnKSueaJpXz9wUX89xljuOakUbhcIZzxHRtrzQU5/nirFPLBB7BkibUJpi/r11uPp56yNtTMnAlFRX1vrFGDiibpAdhYcZDizCTiY7Su6BQThqbx2vdP5EfPr+LONzawaEs1f/r6lNCUP450ZCnkwgvhk09g4cL+bxw2N1uft3ChtbnmuOOs+SLp6aGJWzlWRJU7QrXjcFNlg9ajHSg1PoZ750/ljvMn8dm2Gs66+0Pe8+doLn+lpMCZZ1pdITfcAFOn9r+bEaz5IM8/b3WG3H23VQ7RE2QGrYhaSRtjXgFeKSsruzJY79Ha0cn26ibOmqidHU4kIsyfUci0wiFc/9QyLv+/z/l62TB+PLeU1Ph+dhAGLyirs6O01JpbvWiRdaOxvxPMjYG1a61HXJyV5GfMgPHjvUv2KiJEVJIOhZ3VTXS6jc6QdrixeSm8cv0J3P32Jv7ywRY+3FTFT+eWMntinr3nUaamWqvrM86AzZutTTJLl/Z/IkxrK3z6qfVITbXaAGfMgBEjtH4d4TRJ+2h7tXXKdHGmJmmni4uO4oezx3HGhDxu+ddKrv3HMmaWZHL7vAmMtrszRwRGj7YeF11kJepFi8CbnbL19fDee9YjM9O64Xj00dYBvJqwI44maR9t75oZoZ0d4WPK8HRevf4E/rF4J398awNn3rWQc6cUcP1po53x3zE+3urqmDkT9u8/vGL2ZpdidTW88Yb1yM21NtuUlcHQocGPW4VERCXpUGxm2V7dSFpCDOmJsUF7DxV40VEuvn18MXMn5/PA+1t4YvEOXlqxx0rWp5ZQ7IRkDZCdDfPmwdy5Vjlk8WKrla+5uf+vraiA116zHvn5Vklk+nTr97rCDlsRNWDJo6yszCxZsiQo1/7mXxfT0NrBS9fNDMr1gyZCBiwFSmVDCw9+sJUnPt1Bh9twzpShfO+UEkZmO7Brp70dVq+2EvaqVb7Pr87NhWnTrMfw4ZqwnanX/yiD8/9QP2yvbmR60RC7w1B+ykmJ5ydzS7n6pJH85YOtPPnZDl5cvptzpxbwwzPHkZcWb3eIh8XEWJ0dU6dCUxN88QV89pm1CcabRVZFhbXD8fXXrRr21KkwZYrVy61dIo6nSdoHrR2d7DnQzPnTvNj6q8JCTmo8P51XyrWzRvHQwi387ZMdvLF6H9edUsJ3TxzhvEOGExOtXY3HH2/dQFy2zCqHbN7sXcKurrYGQ739ttXHPXmylbDHj+//kANlC03SPthV04zbwIisfobAq7CTnRLHbXNK+eaxRfzqtXX8/s0NvLJiD/dePM25G5dSU62Z1bNmWaeZL11qPbZs8e7rGxqsFsCPP7a2tU+YAEcdBRMnWglcOYImaR/sqLY6O4q0/S5iFWUm8fC3ynhnXQU3P7eSef/7Eb88dyIXTHf4T0/p6XDaadajttZaYS9das0R8WaF3dZmjV1dvtyqWY8caSXsyZMhL0/r2DaKqCQd7O4Oz5FN2iMd+U4bn8uC75/IDU8v56ZnV7B2Tz0/njM+tEObBmrIkMMJu67ucPLduBHc7v6/3hhrNb5li7U9PSsLJk2yHmPGaFkkxCIqSQd7W/iO6iZS46MZkqh/SQeDvLR4nrzyWH756loe/XgbtU1t3HnB5OAfLhBIaWmHSyKNjbBihXXjce1a78ejVlUd3jwTGwvjxlkJe+JE6zxIFVQRlaSDbXt1I8VZSfZuK1YhFeUSfjavlOyUOH7/5gZqm9r4yzenh+cExKSkwzcdW1utRP3FF1ZbX18HFhyprQ1WrrQeYPVgT5xoPUpKBm1LZzDpd9QH26sbmTJc2+8GGxHhulNKGJIYy60vrOL6p5bzwCXTiA6nFXV3noFNU6daJZDNm61V9ooV1q5Hb+3daz3+/W9rlT12rHUDsrQUcnK0lh0AmqS91NbhZndtM+dNKbA7FGWTi48ppK2jk9tfWcsP/7WSP1xwVHjUqPvjclm15jFj4IILYN8+a3W9cqX3rX1grbJXrbIeYPVke6b/jR1rreSVzzRJe6m8tgm30c6Owe6ymSOoa+7gz29vJD0hlp/OK7U7pMASsUoY+fnWpL7GRqsssnKldT6jt2URsHqyP/zQeohYJ86MH289Ro3S0oiX9Lvkpe1d7XfF2iM96H3/tBJqm9p49ONtjMpJ4pJjiuwOKXiSkg5P2XO7Yds2a4v66tWwc6f31zEGtm+3Hq+/bnWIjB5t3YQcN87arq67H3sUUUk6mC1426t0RKmyiAg/mVvKtqpGfvbSGkZmJXPcqEy7wwo+l+vw0WDnnGPtePScgL52rW+r7Pb2wwcagLWTcuzYww8dCnWIDljy0s9eWs3zy3az8vYzwrO7QwcsBVx9Szvn3fcxNY1tvHTdCRRmDuKfstxua2XtSdrbtnnXk92blJT/TNqRfxNSByz5a1t1E0VZieGZoFVQpMbH8NdvH825933MNU8s5YXrjnferI9QcbmguNh6zJljjVZdvx7WrbMe/R0V1l1DgzWTxLPYSk09fHNzzJhBtQtSk7SXdlQ3MrEgze4wlMOMyErijxcexXcfX8IdC9Zz+9kT7A7JGRISDrf4gXUT0ZOw16+Hgwd9u159/X8m7ZSUwyfbjB5tnUoToTVtTdJe6HQb9hxo1sNnVY++UprL5TOL+b+Pt3P8qEzOmJBnd0jOk5kJJ5xgPYyB8nIrWa9fbx0Z5utp6A0N1nySZcusjxMSrFp5SYmVtIuLI6aUFxl/iiCrbGihvdMwbEiC3aEoh7rlrHF8vr2Gm59bycSCNIam69+VXolY3RzDh8Ppp0Nnp9X1sX49bNhgzQzx9WCD5ubDXSdgJejiYitpl5RYCTwxPO8ZaJL2wu5a6+giTdKqN3HRUdw7fxpfvedDbnl+FX+7/Gi9f+GtqKjDXSNz5lidH9u2WQl7wwbr974m7Y4OayPO5s2Hnxs69PD7jBplHVUWBv+NNEl7oVyTtPJCcVYSt5w1jp++tIbnlpZzYdlwu0MKTzExh28QzptnJe2tW60pfhs3Wknb2+FQR9qzx3p8+KH1cUoK/PjH1phXB9Mk7YXdB6wkXZAenj8uqdD55jFFvLpiL798dS0njckmN9VBx3CFq5iYw614YK2St2+3atmbNlmrZV9r2mCVWdKc3wygSdoL5bVNZCXHkhAbxu1VEdgP70Qul/C7CyYz+66F3PbCah7+1nQtewRadPThWvNZZ1n92Lt2HS5vbNpk3Vjsz6hRWu6IFOW1zRTojSDlpRFZSfz3GWP4zYL1vLW2gjO12yO4XC5rLkhRkXXQgTHWJD9P0t682TqMt7tRo0If6wBEVJIO1rbw3bXNjM9PDeg1VWS7fOYInltazq9eW8vJY7LDc/50uBKxdijm5Fizs8Hqy9661UrYW7ZY5ZIwSdIR1f1tjHnFGHNVWgDrTG63ofxAMwV601D5ICbKxc/mTWBXTTN//XCr3eGo5GTrvMbzz4ebb4a777bKJWEgopJ0MFQ1ttLW4dbODuWzmSVZnDUxj/ve28KerpvPyiGio8Nmh2J4RGkjbb9T/rj1q+NxG8NvFqyzOxQVpjRJ98OzkUXb79RADM9I5OqTRvLqyr0s3VFrdzgqDGmS7odnJa01aTVQV588iuyUOH712loicTSwCi5N0v0or21iSGIMyXER1QijQigpLpqbzhjD8p0HeG3VXrvDUWFGk3Q/dmtnhwqAC6YPZ1xeCr97Yz2tHZ12h6PCiCbpfpTXNjNM69HKT1Eu4bY549lV08zfPtludzgqjGiS7oMxht21upJWgXHi6Gxmjc3mf9/dTG1jm93hqDChSboPNY1tNLd3avudCphbvzqextYO7n5nk92hqDChSboPh3uktdyhAmNMbgrfOLqQJz7dwdb9Ph4hpQYlTdJ9ODyiVFfSKnBuPH0McdEufvv6ertDUWFAk3QfymubAO2RVoGVnRLHtbNG8dbaCj7dWm13OMrhwiJJi8i5IvKwiPxTRM4I1fvurm0mNT6atISYUL2lGiSuOGEk+Wnx/GbBOtxu3eCiehf0JC0ij4pIpYis7vb8bBHZICKbReSWvq5hjHnRGHMlcA3wjWDGe6Q9dS16oKgKioTYKG4+cywry+t4ecUeu8NRDhaKlfRjwOwjnxCRKOA+4CygFJgvIqUiMklEXu32yDniS3/c9XUhsa+uhfw0Pf5IBce5UwqYVJDGbxaso7PX1ywAACAASURBVK55AGf2qUEh6EnaGLMQqOn29AxgszFmqzGmDXgaOMcYs8oYM7fbo1IsvwNeN8YsC3bMHnvrWsjTJK2CxOUSfnPeJKob2/j1a2vtDkc5lF016QJg1xEfl3c915vrga8AF4jINT19gohcJSJLRGTJ/v37/Q6wrcNN1cFW8lK13KGCZ9KwNK4+aSTPLCnnrTX77A5HOVBY3Dg0xtxjjJlujLnGGPOXXj7nIWNMmTGmLDs72+/3rKhvAdByhwq6G74ymokFqdz83MpDbZ9KediVpHcDw4/4eFjXc46xrytJa7lDBVtcdBT3zp9Gp9tw5d+WcLC1w+6QlIPYlaQ/B0aLyAgRiQUuAl7296IiMk9EHqqrq/M7wL11upJWoVOclcR9l0xjQ0UD1z6xlPZOt90hKYcIRQveU8AiYKyIlIvIFcaYDuB7wJvAOuAZY8waf98rkAfR7quzfuzUlbQKlZPHZHPHeZP4cFMVtz6/KugHBNQ2tnHPO5v43pPL+J/nVvL+hko9lMCBgj7J3hgzv5fnFwALgv3+A7W3roXkuGhS4nUjiwqdrx89nPIDzdzzzibSE2O49avjEZGAv88rK/Zw6/OrONjWQVFGItWNbfxzyS7Om1rAHedPIj4mKuDvqQbGqyQtIs8Dj2C1wDn25zARmQfMKwnAUe37tP1O2eQHXxlNXVMbD3+4jegoFz88c2xAE/Xji7bz05fWcHTxEH593iTG5KbQ2tHJgx9s5U//3kh9czsPf6sMlyvw/zgo33lb7rgfuBjYJCK/FZGxQYxpwAJZ7tirG1mUTUSE28+ewMXHFPLA+1v48783Buzan26t5vaX1/CV8bn8/YpjGJObAlg3L79/2mhun1fKO+sreeCDLQF7T+Ufr5K0MeZtY8wlwDRgO/C2iHwiIpeLSETWA/bVtZCXqkla2UNE+NU5E/lG2XDueXcz9wRg/nRNYxs3PL2coswk7rpoSo8ljW8fX8y8o4byp39vZHOljlJ1Aq9vHIpIJnAZ8F1gOXA3VtL+d1AiG4BAdXd0dLqpbNCVtLKXyyXccf4kzp9WwJ/+vZH739884GsZY7jp2RXUNrZz78VTez1YWUT42bxSEmKi+N0bOkrVCbxK0iLyAvAhkAjMM8acbYz5pzHmeiA5mAH6IlDljv0HW3EbyEvT3YbKXi6X8PsLjuKcKUO5840NPLxw64Cu88hH23h3fSW3zRnPhKF9//+RlWyNUv332go+3959ooMKNW9X0g8bY0qNMXcYY/YCiEgcgDGmLGjR2UR7pJWTRLmEP154FHMm5/PrBet49KNtPn39il0H+N0b6zmjNJdvHVfk1dd8Z+YIhiTGDPgfBRU43ibpX/Xw3KJABuIk++p0t6FylugoF3d9YwqzJ+Txi1fX8tRnO736uvqWdq5/ajk5KfHcecFkr7tEEmKjmD+jkLfXVbCrpsmf0JWf+kzSIpInItOBBBGZKiLTuh6zsEofjhKomrSupJUTxUS5uGf+VGaNzebWF1bxSj9zqI0x3Pr8KnYfaObui6aQnhjr0/tdelwRIsLji7YPPGjlt/5W0mcCf8CarfEn4I9djxuBW4Mbmu8CVZPeV9dMfIxLT2RRjhMb7eKBS6ZzdFEGP/jnF7y7vqLXz3304+28unIvN54+hrLiDJ/fKz8tgdPH5/LC8t106DZ12/SZpI0xfzPGnAJcZow55YjH2caY50MUY8hZPdIJQdnppZS/EmKjeOSyMsbnp3LN35fx4vIvzyZ7ecUefvXaWmZPyOPak0cN+L3OnTqUqoNtfLJFz2K0S587DkXkm8aYJ4BiEbmx++vGmD8FLTIb7atrITc1zu4wlOpVSnwMT1xxDFc/sYT/988veH9DJd85YQSJsVE89dkuHvloG2VFQ7jroil+7RycNTaHlPhoXvxiNyeN8X8EsPJdf9vCk7p+dUybXSjsrWthxgjffzxUKpTSEmN4/DvHcPc7G3n4w228+MXhGvX8GYX8bF6p3zM44mOiOGtiHq+t3EvLeZ0608MGfSZpY8yDXb/+PDTh+CcQszvcbkNFvc7tUOEhNtrFzWeO41vHFbN0Ry31ze2cMDqLYUMCd19/zuShPLOknE+2VHHquNyAXVd5x9vNLHeKSKqIxIjIOyKyX0S+GezgfBWIG4dVja10uI12dqiwkpsaz1cn5XPRjMKAJmiAY0ZkkBgbxTvrKgN6XeUdb/ukzzDG1ANzsWZ3lAA3BysoOx3qkda5HUoBVsnjhJIs3l2v86bt4G2S9pRF5gDPGmP8P/rEoQ73SOuWcKU8vjI+l711Lazb22B3KIOOt0n6VRFZD0wH3hGRbKAleGHZx3MAbW6adnco5TFrnNXZ8d4GLXmEmrejSm8BjgfKjDHtQCNwTjADs0tlfSsugcwkTdJKeeSkxDMuL4VPtlTZHcqg48vxWeOw+qWP/JrHAxyPXwLR3VHZ0EJWchxReiqFUv/huFGZPLl4Jy3t2ooXSt52d/wda3v4CcDRXQ/HTb8LRHdHZUMrObqRRakvOX5UFq0dbpbvPGB3KIOKtyvpMqDUDIJbu5X1rdojrVQPZozIwCWwaEsVx43KtDucQcPbG4ergbxgBuIUlQ2t5KToSlqp7tISYphUkBaWczzqW9pZs6eO6oOtdofiM29X0lnAWhH5DDj0pzTGnB2UqGzS0emmulGTtFK9OWZkJo99vJ3Wjk7iop1fl27rcHPve5u5/73NdLgNsVEuzp06lJ+fPZGEWOfHD94n6duDGYRTVDe2YQxk60YWpXo0rXAIDy3cyurd9UwvGmJ3OH1yuw3XP7WMN9dUcO6UoZxemsdn26p5/NMd7Kpp5pHLykiM9aV3wh5eRWiM+UBEioDRxpi3RSQRCI9/hnxQWW/9kKAraaV6Nq0oHYBlO2odn6TveXcTb66p4MdzxvPdE0cCMGdyPlMLh3DjM19w+8truPOCo2yOsn/edndcCTwHPNj1VAHwYrCCGih/T2apbLA2smiSVqpnOSnxFGYksnRHrd2h9GnDvgbueWcT508t4IoTRvzHa+dOLeCqk0bxzJJyPt7s/L5vb28cXgfMBOoBjDGbgJxgBTVQ/rbgVTZ0raS13KFUr6YXDWHpzlpHz/H49YJ1JMdF85O5pT0e3vH/vjKakVlJ/OTF1XS6nfvnAO+TdKsxps3zQdeGFmf/yQbAU+7ITtaVtFK9mVY0hP0NreyqabY7lB59srmKhRv3c/2poxmS1PO5jvExUdx85li2VjXy+uq9IY7QN94m6Q9E5FasA2lPB54FXgleWPaobGhhSGIMsdHefluUGnymDrfq0ivKnbmp5dGPt5GZFMulxxX1+XlnTshjVHYS9723xdE/FXibjW4B9gOrgKuBBcCPgxWUXaweaS11KNWXMbkpxEa5WL3becMwd1Y38c76SubPKOx367rLJVxz8ijW7a1nkYN7v70dsOTGulH4X8aYC4wxD0fi7kPdEq5U/2KjXYzPT2FlufOS9BOLd+AS4ZvH9r2K9ph31FBS4qN5dml5kCMbuD6TtFhuF5EqYAOwoetUlp+GJrzQ2l/fQrZ2dijVr4kFaazeXYfbQTfdOt2GF5bv5rRxOV6PdoiPiWLeUUN5ffVeGlragxzhwPS3kv4BVlfH0caYDGNMBnAMMFNEfhD06ELIGMP+g1ruUMobk4el0dDawY6aJrtDOWTxtmr2N7RyzpQCn77uwunDaGl389pKZ95A7C9JXwrMN8Zs8zxhjNkKfBP4VjADC7XapnbaO432SCvlhUkF1s3DlQ66efjKij0kxkZx6jjfuoOnDE9nRFYSr60KzyQdY4z5Ure3MWY/EBOckOxxaCOL1qSV6tfo3GRio51z87C9083rq/dxemmuzzM5RIQzJuSyaEs1dc3OK3n0l6TbBviaLfzZcXh4S7iWO5TqT0yUi3F5KazdW293KAAs2V7LgaZ2zpqYP6CvP6M0jw634X0HHg/WX5I+SkTqe3g0AJNCEaAv/NlxeGi3oZY7lPLK+LxU1u1tcESP8fsbKomJEk4YnTWgr586PJ2s5DjeWlsR4Mj812eSNsZEGWNSe3ikGGO03KHUIDYuP4Waxjb2N9g/o/m9DZXMGJFBctzAptq5XMLppTm8v76S9k53gKPzj26t61JZ30pyXHRYjC5UygnG56cCsG5fg61xlNc2sbHiIKeM9W+c0Mljsmls62TFLufcDAVN0ofs1xNZlPLJ+LyuJG1zXfqDjfsBmDU226/rHDcyCxH4yGGT8TRJd6ls0I0sSvkiLTGGoWnxrLc5SX+ypZr8tHhGZSf7dZ20xBgmF6Q5bnypJuku1pZw7exQyhfj8q2bh3YxxrB4azXHjszscSSpr2aWZLF85wEOtnYEILrA0CSN9R+6sl7LHUr5anx+Clv2H6Stw56bbVv2N1J1sI1jR2YE5HonlGTR4TZ8ts05A5c0SQMHWztobu/UJK2Uj8bkptDhNmyvbrTl/T/daiXTY0dmBuR6UwuHEO0SPt/unJNnNElz5IksmqSV8kVJjlUH3lRx0Jb3/3SrVY8uzEgMyPUSYqOYWJDGUk3SzlKYkcj7N83i1HG5doeiVFgZlZ2MS2BjRejr0sYYPt9ew4wRGQGpR3uUFQ1hRfkBWjs6A3ZNf2iSxtriWpyVRFpCRO3PUSro4mOiKMxIZHNl6FfSe+taqKhvZVphYE8tLyseQmuHm9W7nbHlXZO0UsovJTkpbKoM/Up6+U5r08nUwvSAXnd6kXUTcumOmoBed6A0SSul/DI6N5ltVY0h3069fGctcdEuxnVtqgmU7JQ4ijITWeKQurQmaaWUX8bkJtPeadgR4g6P5bsOMKkgLSgHR08Znu6Y48Ecn6RFZLyI/EVEnhORa+2ORyn1n0bnpACwMYQdHm0dblbtrgt4qcNj8rB09tW3UFnfEpTr+yKoSVpEHhWRShFZ3e352SKyQUQ2i8gtfV3DGLPOGHMN8HWso7yUUg4yMjsJgK37Q5ek1++rp63DzZThgb1p6DF5mDXu2Amr6WCvpB8DZh/5hIhEAfcBZwGlwHwRKRWRSSLyardHTtfXnA28BiwIcrxKKR8lxkaTnxbP1v2hK3es6joRxpNMA23C0FRcAisdcPJMUOdyGmMWikhxt6dnAJu7zkpERJ4GzjHG3AHM7eU6LwMvi8hrwJM9fY6IXAVcBVBYWBiQ+JVS3hmZncSWqtAl6dW760mNj2bYkISgXD8xNprROSmOOMPRjpp0AbDriI/Lu57rkYjMEpF7RORB+lhJG2MeMsaUGWPKsrP9G1molPLNiKwktu0/GLJTWtbsqWNiQVpAN7F0N3lYGivL62w/ecbxNw6NMe8bY75vjLnaGHOf3fEopb5sZFYy9S0dVDcG/+jT9k436/c2MLEgOKUOj8nD0qhpbGNPnb03D+1I0ruB4Ud8PKzrOb/5cxCtUmrgDt88DH7JY1PFQdo63UwYGtj+6O5Ku66/bo+9Ow/tSNKfA6NFZISIxAIXAS8H4sL+HESrlBo4z8D9UHR4rN5jLcKCvZIe65CTZ4LdgvcUsAgYKyLlInKFMaYD+B7wJrAOeMYYsyaYcSilgmtoegKx0S62huDm4do99STGRjEiMymo75McF01RZiLr9tmbpIPd3TG/l+cXEIR2OhGZB8wrKSkJ9KWVUn2IcgnFmYkhWUmv21vP2LwUXK7g3TT0GJ9n78kzEAY3Dn2h5Q6l7FOcmcSO6qagvocxhg0VDYzLSwnq+3iMz09le3UjTW32HacVUUlaKWWfosxEdtY0BbVlrbKhlQNN7YzNDVWSTsEYWL/PvtW0JmmlVEAUZiTS2uE+dNJRMHiS5dgAT77rzfh8+28eRlSS1hY8pexT2HUjL5gljw1dN/FCVe4YNiSB5LhoNupKOjC0Jq2UfTznDO6sCV6SXr+vgZyUOIYkxQbtPY4kIpTkJId0wl93EZWklVL2KUhPwCWwM4hzpTfsa2BsiFbRHmNyk9lkw/FgHpqklVIBERvtIj8tIWgr6U63YVPlwZCVOjxG56RQdbCV2hBsee9JRCVprUkrZa+izER2BClJ76ppoq3DfeiQgVAZnWvtprTjRHSIsCStNWml7FWYkciuICVpz4nko3KCu9OwuzFd7X52lTwiKkkrpexVmJlI1cE2DrYGfvPH5q7djCXZoV1J56fFkxwXzSZdSSulwp2nwyMYq+nNlQfJSo4jLTEm4Nfui90dHhGVpLUmrZS9ijKC1yu9ufIgJSEudXiMzkk+tJIPtYhK0lqT7oPNp0uowSFYK2ljDFsqD1KSkxzQ63prZHYy+xtaaWhpD/l7R1SSVj4K4tFDanBKS4whLSGGHTWB7ZWubGilobWDkmy7knToDjXoTpO0UiqgrEFLzQG9pqezoyTE7XceozxJuir0JQ9N0kqpgBqekRjwXYeeOdWhbr/zKMxIIsolupJWSoW/ooxEymub6eh0B+ya26qaSIiJIi81PmDX9EVstIvhQxI0SftLuzuUsl9hRiIdbsPeAJ6yva3qIMVZSYiN91FGZiezxYYOj4hK0trdoZT9CjMDPw1vW1UjI7ISA3a9gRiZlcT26kbc7tB2SkVUklZK2S/QI0vbO93sqm1mRJY99WiPkdnJtLS72VMX2Jui/dEkrZQKqPy0BKJdErAkvaumiU63YUSWPe13Hp5/JLaF4ET0I2mSVkoFVJRLyEuLZ++BwKw4t3d1ithd7igKQhnHG5qklVIBV5CewJ4Dgblx6OmosHslnZcaT2yUi51BPhG9O03SSqmAK0hPYHeAVtLbqhpJjY9mSIgHK3XncgnDMoJ3qEGv7xvSd1NKDQpD0xPYV98SkF7pHdVNjLC5/c6jKCMxqAft9iSikrT2SSvlDEPTE+h0GyobWv2+1s6apkMnkdvNc6iBCeHAsohK0tonrZQzDE23dgbu8bPk0dHpZveBZgozEgIRlt8KM5NoaO2gtil00/AiKkkrpZyhIN1Kqv7WpffWtdDpNgwfYm9nh0dRVw/4jiCeiN6dJmmlVMDldyVpfzs8PHOpPRtk7BaM3ZT90SStlAq45Lho0hJi/C537Kq1kuFwpyRpz27KEN481CStlAqKoekJfifpnTVNRLmE/DR7pt91Fx8TRW5qHDt0Ja2UCneB6JXeVdPM0PR4oqOck6oKMxK13KGUCn8F6fF+J+mdNU2OqUd7FGYkablDKRX+hqYn0NDSQb0fh7eW1zY5prPDoygzkX31LbS0d4bk/TRJK6WCYmhXh8feAXZ4NLZ2UHWwzTE3DT08K/vy2tCspiMqSeuOQ6WcY+ihNryBlTw8nR2OK3dkenqlNUn7THccKuUc/m5o2dV14rhTV9KapJVSYS07JY5olwx4Jb3TYRtZPDKTYkmKjQpZh4cmaaVUUHiG/w+43FHTRFJslO0jSrsTEQozkzRJK6XCnz+90rtqmhiekeiIEaXdFYZwrrQmaaVU0PhzQsuu2ibH1aM9irpW0qE4OVyTtFIqaAY6/N8Yw66aZsfVoz0K0hNo63BT3dgW9PfSJK2UCpqBDv+vOthGc3snw4c4Y450d/62F/pCk7RSKmg8w/99rUsf6uzIdOZKOlCHGnhDk7RSKmjy06wV57463+rS5Q7dyOIRqEMNvKFJWikVNHmp1orT1yTtGfY/zGFzOzzSEmJIjI3y+1ADb2iSVkoFTWpCNAkxUeyr9y2Z7T7QQmZSLPExUUGKzD8iEpB52d7QJK2UChoRa0OLr0l6z4HmQzfnnGpoegJ76jRJK6XCXF5qvM/ljr11zYduzjlVQfrAd1P6QpO0Uiqo8tJ8S9LGGHbXNh+66ehUQ9MSqDrYFvS50mGRpEUkSUSWiMhcu2NRSvkmLy2eivoWr3fn1bd00NjWeaiDwqkOzcv28acEXwU1SYvIoyJSKSKruz0/W0Q2iMhmEbnFi0v9D/BMcKJUSgVTXmo8HW7j9e48TwnB6TXpgiGh2dASHdSrw2PAvcDjnidEJAq4DzgdKAc+F5GXgSjgjm5f/x3gKGAt4OwClVKqR3lph9vwslPi+v38vXWeJO3s/+VD1Ssd1CRtjFkoIsXdnp4BbDbGbAUQkaeBc4wxdwBfKmeIyCwgCSgFmkVkgTHmS4MAROQq4CqAwsLCAP4plFL+ONQrXd/CJPo/kGN3V++x01fSuanxiIT/SronBcCuIz4uB47p7ZONMbcBiMhlQFVPCbrr8x4CHgIoKysL/mgqpZRXDq2kvWzD23OgmZgoITu5/1W3nWKjXeSkxEVkkh4QY8xjdseglPJdVnIcUS5hn5c9xXsONJOXFo/L5bw50t0N9WMUq7fs6O7YDQw/4uNhXc/5TQ+iVcp5olxCTkoc++q8m4S390ALQx3efucRil2HdiTpz4HRIjJCRGKBi4CXA3FhPYhWKWeydh16l8x2h8FuQw/PyTPGBK/CGuwWvKeARcBYESkXkSuMMR3A94A3gXXAM8aYNcGMQyllL293HXa6DfvqWxzf2eExNC2e1g43NUEc/h/s7o75vTy/AFgQ6PcTkXnAvJKSkkBfWinlh7y0eBZu3N/v5+1vaKXTbcJmJX14+H8LmUG60RkWOw69peUOpZwpLzWexrZOGlra+/w8T89xONWkIbi90hGVpJVSznTkhpa+hMtuQ4+CEByjFVFJWrs7lHKmIze09OVwkg6PmnR6YgwJMVGapL2l5Q6lnMnbY7T21rWQEh9NSnxMKMLymzX8P17LHUqp8JaTat1U6y9J7z7QHDb1aI+h6QlBnYSnSVopFXTxMVEMSYzxqtwRLqUOj5yUeCp9PHnGFxGVpLUmrZRz5aUleHXjMFxuGnrkpcVR2dDq9bxsX0VUktaatFLOlZca1+dKurmtk9qm9rBL0rk+zsv2VUQlaaWUc/W3kt4TJnOku8vt6lypCFLJQ5O0Uiok8lLjqW5so7Wj5zMB94TZRhYPT5L29bBdb2mSVkqFRH7XhpbK+p6n4e0Nk2H/3Xl6wCsaNEn3S28cKuVcuf0M/999oBmRw7sTw0VWciwugQpdSfdPbxwq5Vz5/WwN33OgmZyUOGKiwistRUe5yEqOo6KXnxD8FV7fDaVU2OqvdrunLvza7zysedm6klZKhbHU+GgSY6N6TWZ7D7SEbZLOSYnX7g6lVHgTkV6H/xtjuraEh1c92iMvLU6TtFIq/OWm9lwWqGlso7XDHbYr6dyUeGqb2mlp77m90B8RlaS1u0MpZ8tP63klvSdM2+88PJ0r+xsCf/MwopK0dnco5Wy5aVbttvuci0O7DcNsI4tHrpfzsgciopK0UsrZ8tN6nnMRbsP+u8sL4tZwTdJKqZDprQ1vz4Fm4qJdZCTF2hGW3/KCuDVck7RSKmTye9l1WF7bTMGQBETEjrD8lpoQTVy0S1fSSqnw5jlGa3dt0388v726iaKMRDtCCggRIS8tPii7DjVJK6VCJis5lsTYKHbUHE7Sxhh2VjdSlJlkY2T+y00Jzq7DiErS2oKnlLOJCIUZieysPpykqxvbaGzrpDCMV9Jgda4E4xitiErS2oKnlPMVZSb+x0p6R1fCLsoM8ySdYp08Y0xgj9GKqCStlHK+oswkdtY0HeqV3lnT2PV8eCfpvLR4Wtrd1Ld0BPS6mqSVUiFVmJFIW4f70JD8HdVNiMCwIeGdpHOC1CutSVopFVLFXTcIt1dZZY6d1U3kpcYTHxNlZ1h+C1avtCZppVRIecoanjLHjpqmsL9pCMHbdahJWikVUvlp8US75NANwx3VTWFfjwbISY0DAp+kowN6NaWU6kd0lIthQxLYUdPErpomqg62MiY3xe6w/BYfE8VDl05nXF5qQK+rSVopFXLj8lL5fFsNb6+rAOCUcTk2RxQYZ0zIC/g1tdyhlAq5c6cWUNnQyv++u5nizERGZoX3bsNg0iStlAq508bnkJUcS01jG6eOyw3bwUqhEFFJWreFKxUeYqJcnDe1ALAStupdRNWkjTGvAK+UlZVdaXcsSqm+XXPyKLKS4zh2ZKbdoThaRCVppVT4yEyO4+qTR9kdhuNFVLlDKaUijSZppZRyME3SSinlYJqklVLKwTRJK6WUg2mSVkopB9MkrZRSDqZJWimlHEyTtFJKOZgmaaWUcjBN0kop5WCapJVSysHEGGN3DAEnIvuBHXbH0U0WUGV3EA6g34fD9Hth0e8DVBljZvf0QkQmaScSkSXGmDK747Cbfh8O0++FRb8PfdNyh1JKOZgmaaWUcjBN0qHzkN0BOIR+Hw7T74VFvw990Jq0Uko5mK6klVLKwTRJK6WUg2mSDgERmS0iG0Rks4jcYnc8dhCR4SLynoisFZE1InKD3THZSUSiRGS5iLxqdyx2EpF0EXlORNaLyDoROc7umJxGa9JBJiJRwEbgdKAc+ByYb4xZa2tgISYi+UC+MWaZiKQAS4FzB9v3wUNEbgTKgFRjzFy747GLiPwN+NAY81cRiQUSjTEH7I7LSXQlHXwzgM3GmK3GmDbgaeAcm2MKOWPMXmPMsq7fNwDrgAJ7o7KHiAwD5gB/tTsWO4lIGnAS8AiAMaZNE/SXaZIOvgJg1xEflzNIk5OHiBQDU4HF9kZim7uAHwJuuwOx2QhgP/B/XaWfv4pIkt1BOY0maRVSIpIM/Av4f8aYervjCTURmQtUGmOW2h2LA0QD04AHjDFTgUZgUN6z6Ysm6eDbDQw/4uNhXc8NOiISg5Wg/2GMed7ueGwyEzhbRLZjlb5OFZEn7A3JNuVAuTHG8xPVc1hJWx1Bk3TwfQ6MFpERXTdGLgJetjmmkBMRwao9rjPG/MnueOxijPmRMWaYMaYY6+/Cu8aYb9ocli2MMfuAXSIytuup04BBeSO5L9F2BxDpjDEdIvI94E0gCnjUGLPG5rDsMBO4FFglIl90PXerMWaBjTEp+10P/KNrAbMVuNzmeBxHW/CUUsrBtNyh7noxaAAAApVJREFUlFIOpklaKaUcTJO0Uko5mCZppZRyME3SSinlYJqkVcQQkYN2x+ANEbldRG6yOw4VHjRJK6WUg2mSVhFHLL8XkdUiskpEvtH1vEtE7u+aXfxvEVkgIhd0vfbbrlnXK0XkD13PzRORxV3Df94Wkdyu528Xkb+JyIciskNEzheRO7ve642u7e+IyPYjnv9MREp6iHVU19cs7breuNB9p1Q40CStItH5wBTgKOArwO+75lmfDxQDpVi7H48DEJFM4DxggjFmMvCrrut8BBzbNfznaazJdR6jgFOBs4EngPeMMZOAZqwxpB51Xc/fizX9rruHgOuNMdOBm4D7/fqTq4ij28JVJDoBeMoY0wlUiMgHwNFdzz9rjHED+0Tkva7PrwNagEe6TkrxnJYyDPhnV4KPBbYd8R6vG2PaRWQV1nb/N7qeX4X1D4HHU0f8+ucjg+yaCHg88Kw12gSAuAH/qVVE0pW0GvSMMR1YhzM8B8zlcML9X+DerpXw1UD8EV/W2vW1bqDdHJ6v4OY/Fz+ml9+D9f/fAWPMlCMe4wPxZ1KRQ5O0ikQfAt/oOkcwG+v0j8+Aj4GvddWmc4FZcGhFm9Y17OkHWGUSgDQOj5X99gBj+cYRvy468oWuedrbROTCrjhERI5CqSNouUNFohew6s0rsFavPzTG7BORf3F4HOYuYBlWqSMFeElE4gEBbuy6zu1YpYha4F2sk0R8NUREVmKtvOf38PolwAMi8mMgBqv2vWIA76MilE7BU4OKiCQbYw523Sz8DJjZNdc4GO+1HSgzxlQF4/pqcNCVtBpsXhWRdKwbgb8MVoJWKlB0Ja2UUg6mNw6VUsrBNEkrpZSDaZJWSikH0yStlFIOpklaKaUc7P8DF+9jRKWEv9UAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"# bounded inverse transform sample"
],
"metadata": {
"id": "pkrYcoiDhb_g"
}
},
{
"cell_type": "code",
"source": [
"lower_bound, upper_bound = 3.0, 10.0"
],
"metadata": {
"id": "_kQFF3VxhnKM"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from inverse transform sampling\n",
" data = pd.DataFrame.from_records([{\n",
" 'sample' : bounded_pareto_inverse_transform_sample(alpha=alpha, lower_bound=lower_bound,upper_bound=upper_bound),\n",
" } for __ in range(10000)])\n",
" sns.displot(data=data, x='sample', kind='ecdf')\n",
" print(data['sample'].min(), data['sample'].max())\n",
"\n",
" # expected\n",
" x = np.geomspace(data['sample'].min(), data['sample'].max(), 100)\n",
" plt.gca().plot(x, bounded_pareto_cdf(x, alpha=alpha, lower_bound=lower_bound, upper_bound=upper_bound),'r-', lw=5, alpha=0.6)\n",
"\n",
" plt.gca().set(xscale=\"log\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "xFarqW1LhexR",
"outputId": "b92db45d-3af9-4f94-c1cf-3b9fe95bf740"
},
"execution_count": null,
"outputs": [
{
"output_type": "stream",
"name": "stdout",
"text": [
"3.000345322156993 9.99773932161884\n",
"3.0005454483861724 9.999369587024335\n",
"3.0000305330481547 9.993724059212868\n"
]
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from inverse transform sampling\n",
" data = pd.DataFrame.from_records([{\n",
" 'logsample' : np.log(bounded_pareto_inverse_transform_sample(alpha=alpha,lower_bound=lower_bound, upper_bound=upper_bound)),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='logsample', kind='kde')\n",
"\n",
" # expected\n",
" x = np.linspace(data['logsample'].min(), data['logsample'].max(), 100)\n",
" plt.gca().plot(x, bounded_pareto_pdf(x, alpha=alpha, lower_bound=lower_bound, upper_bound=upper_bound), 'r-', lw=5, alpha=0.6)\n",
"\n",
" plt.gca().set(yscale=\"log\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"id": "0O5mTHHRhw19",
"outputId": "d54fbed8-a58c-4314-e34d-31735c9069bc"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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0sK2una4Bb1OmwuwMVlUWsWRmIUtnFbB0dgE15fnB29HQOW9qpL4eGhrOf4zlqBu80fXMmV5o3367t4dJcrhoSAfsv7xc6Puvn6S2tZev/cEGBXSSMDMWzyxg8cwCPnTDfEIhx/HWXrafbGfHyXb2NXbx6Ot1DAyfD7vS/Cwqi3OpKsllzvQcZuRlUZyXRUleJkU5WUzLSDt3jcqMNGMk5BgaCXnH6CiDIyEGh0P0D4/SNzRK/9AIfUPhz4dH6RvyLkScme49z7SMdLIz0ygvyGZ2UTaVxTnML807//+gmdeWV1wMq1ad/+FGRrygbmh449HeHp03LxTyVmOePg033RSd5wy4pBpJJ9tilqGREDf+w4tUleTw+Eeu1fajKWQ05Khr6+VQUzfHWrwLJdR39HHqbD+nO/sZHo3e7+20jDRys9LJykhjeHR8uIf+w/2Wzi5kfXUxtywtY9P8EqZlRDj10N/vTZk0NJz/ePq0Nwd+pT7/eShMmi4nTXckose3nuJTT+zmmw9u5OYl5X6XIwHhnKNncIT23mHO9g3R2T98LliHR71wzUw3stK94M3KSCMrPY1pmV4Y52ZmkJOV7h2Z6Rfd92V4NERL9yCnOweoa+tlX2MX+xo72XGyg8GRELlZ6dyxYhYPXF3NhrlXeO3M7m4vrMdCu7HROy63vWtuLnzhC8m0aZRCOtGEQo7bvvgSWRnpPPunN2gULYHRPzTK5uOtvLC/mWd2NdI9OMLimfl87JYa7lpdMfUTn86dD+/GRm/6ZOxjl9fWyMKF8KlPTf2HCQ6FdKL5+b4mPvKdbXzp/nXcvabC73JEJtQ3NMIzu07zjd/WcrCpm6WzCvjkHUu4ddnM2Lxgb+/5k5OLFsXmNfyhkE4kzjne8eXf0d47xK/+/CadMJTAC4UcP91zmi+8cJja1l7eumoWf3v3SsoKpvldWqK4aEjrtz+AXqs9y65THTx04wIFtCSEtDTjrjUVPP+JG/nkHUv4xf5mbvviSzyzO0pXV09hSoAA+vbmE0zPzeTe9ZV+lyIyKZnpaXzslhqe/fgNzJuRx8OP7uB/PXuAkdEY9k4nOYV0wDR3D/D8vjO8Z30l2ZlJubJKUkBNeQGPf+Ra/uDauTzy8nE++P+20NE35HdZCUkhHTA/2FrPSMhx/yYt/5bElpWRxv+4ZyX/+92reL32LPd99VVaumOwZWqSU0gHyGjI8ehrJ7lu4QwWlGlPXkkO922s5psPbuTk2T7ue2QzTZ1RvOhuClBIB8jLR1po6Ojn96+e63cpIlF1XU0p3/7QJpq7BnnvVzdzurPf75IShkI6QP791ZOU5mdx2/IY9ZiK+GjjvBK+++Grae8d4sH/t4WugWG/S0oISRXSZnaXmT3S2dnpdymT1tQ5wK8OnuG9G6rIykiq/ywi56ytms6/vn89R5t7+OPvbmdoRF0fl5NUaeCce9o591BRUZHfpUzaU7saCDl4z4Yqv0sRiakbFpXy9+9ezStHW/nMj/aQjAvqoklblQbEkzsbWVNZ5P/18ETi4N71lZw628c//vIIa6un84FrdB7mYpJqJJ2ojjZ3s6+xi3vWzvG7FJG4+fiti7h5SRl/9/R+9jYk3hRlvCikA+DJnY2kGbx9zWy/SxGJm7Q04wvvXUtJXhYPP7qdbp1InJBC2mfOOZ7c2cj1NaWUF2T7XY5IXJXkZfFPD6zjVHs/f/XjvX6XE0gKaZ/tONXBybN92o5UUtbGeSV8/NZFPLWrkef3NfldTuAopH325I4GsjLSuHPlLL9LEfHNH928kKWzCvhvT+5V//QFFNI+Gg3vwXvr0nIKsjP9LkfEN5npafzDvatp6R7kc88e9LucQFFI+2j7yXZae4Z46yqdMBRZXTmdD79pAd97/SSbj7X5XU5gKKR99Py+JrLS07h5SZnfpYgEwifevJiqkhw++9Q+RkNa5AIKad8453h+/xmuq5mhqQ6RsJysdD7zlmUcOtPNY1tO+V1OICikfXL4TA91bX3cvlwnDEXGe8vKWWycV8wXXjik3mkU0r75+b4mzODNy8v9LkUkUMyMv37bclp7hvjXXx/zuxzfKaR98vz+JtZVTdcCFpEJrKmazjvXzeFrr9RS397ndzm+Ukj7oKGjn70NXdy+QlMdIhfzyTuWgIN/eTG1R9MKaR+8EF5VdYdCWuSiKqbn8N6NlTyx7RQNHal7JReFtA9+caCZmvJ8bUsqchl/dHMNAF9J4bnpwIe0mS0ws6+b2RN+1xINfUMjvF57lpsXqzda5HLmTM/h3vVVPLblVMpeFzGmIW1m3zCzZjPbe8Htd5rZITM7amafvtRzOOeOO+c+FMs64+m142cZGg1xkxawiETkj29eSMg5vvrScb9L8UWsR9LfBO4cf4OZpQP/ArwFWA7cb2bLzWyVmT1zwZF0/WkvHW4hOzONjfNK/C5FJCFUleTy7qsqefT1k7R0D/pdTtzFNKSdcy8DZy+4eRNwNDxCHgK+D9zjnNvjnHv7BUdzpK9lZg+Z2VYz29rS0hLFnyK6XjrcwjULZpCdme53KSIJ46GbFjA0EuLR1076XUrc+TEnPQcYv96zPnzbhMxshpl9BVhnZp+52P2cc4845zY45zaUlQVzKuFkWx+1rb3cpPlokUlZWJbPLUvK+M6rdQyOjPpdTlwF/sShc67NOfdR59xC59zn/K5nKl464o3wb1RIi0zaf75hPq09g/x092m/S4krP0K6Aaga93Vl+LYpM7O7zOyRzs5gXtTypUMtVBbnsECtdyKTdkNNKYvK8/n6K7U4lzo75PkR0luARWY238yygPcBT0XjiZ1zTzvnHioqKorG00XV0EiIzcdauXFxGWbmdzkiCcfMePD6+exr7GLLiXa/y4mbWLfgfQ/YDCwxs3oz+5BzbgR4GPg5cAB43Dm3L5Z1BMG2unZ6h0Y1Hy0yBe9cN4fpuZl845Vav0uJm4xYPrlz7v6L3P4s8GwsXztoXjnaQnqacd3CGX6XIpKwcrLSuW9DFV97pZbm7oGU2KAs8CcOJyPIc9KvHj/LqjlF2uBfZIreu7GK0ZDjR9ujcior8JIqpIM6J907OMKuUx1cq1G0yJQtLMtn47xiHt9yKiVOICZVSAfVtrp2RkKOaxYopEWi4b0bqjje2psSJxAV0nGw+XgbGWnGhrnFfpcikhTetno2+dMyUuI6iEkV0kGdk958rI01VdPJmxbT87QiKSM3K4O71lTw0z2NdCX5dRCTKqSDOCfdMzjCnoZOrlmgDZVEoum+jVUMDId4elej36XEVFKFdBBtOXGW0ZDj2gWlfpciklTWVBaxqDyfn+xI7i4PhXSMvXq8jcx0Y73mo0Wiysy4e00FW060J/XltRTSMfbqsTbWVk0nJ0tbk4pE211rKgB4JomnPJIqpIN24rB7YJg9DZ1cq9Y7kZiYV5rHmsoinlJIJ4agnTjcVtdOyMHVCmmRmLlrTQX7Grs41tLjdykxkVQhHTTb6tpJTzPWVk33uxSRpHXXmgrM4KmdyTmaVkjH0NYT7SybXaD+aJEYmlmYzdXzS3h6V2NSLhNXSMfIyGiInac62DBX/dEisXb3mjkcb+1lX2OX36VEXVKFdJBOHB443U3/8Kha70Ti4C0rZ5Fm8NzeJr9LibqkCukgnTjcWuddJF0hLRJ7xXlZbJpfwvP7FdISoW117VQUZVMxPcfvUkRSwu3LZ3H4TA+1rb1+lxJVCukY2VbXzvp5mo8WiZfbls8E4IUkG00rpGOgoaOf050DrK9W651IvFSV5LJ8diHP7zvjdylRpZCOgW113kbkGzSSFomrO1bMYtvJdlq6B/0uJWoU0jGw7cRZcrPSWTqrwO9SRFLK7Stm4hz88kDyjKaTKqSD0oK3ta6dtVXTyUhPqrdXJPCWziqgqiSH5/crpAMpCC14/UOjHGzq5qpqtd6JxJuZcfvyWbxypJXewRG/y4mKpArpINjb2MloyGm/DhGf3LqsnKHREL871uZ3KVGhkI6yXac6AFhd5f+CGpFUtGFuCXlZ6fz6ULPfpUSFQjrKdtV3UlGUTXlBtt+liKSkrIw0rqsp5aXDLUmx4ZJCOsp2nepgjaY6RHx10+Iy6tv7OdaS+KsPFdJRdLZ3iJNn+xTSIj67aXEZAC8dbvG5kqlTSEfR7vrwfHSl5qNF/FRVksvCsrykmJdWSEfRrlOdmMGqOQppEb/dvKSc12rP0j806ncpU5JUIe33YpZd9R3UlOVTkJ3py+uLyHk3LS5jaCTEq8cTuxUvopA2sx+Z2dvMLNCh7udiFuccu051sLpS89EiQbBpfgk5mYnfihdp6H4ZeAA4YmZ/b2ZLYlhTQmro6Ketd4i16o8WCYTszHSuWVDCy0da/S5lSiIKaefcL5xzvw9cBZwAfmFmvzOzB81Mf9vjzUcD6uwQCZDra0qpbe2lsaPf71KuWMTTF2Y2A/gg8GFgB/CPeKH9QkwqSzC76jvISk9j6axCv0sRkbDrFpYCsDmBl4hHOif9Y+A3QC5wl3PubufcY865PwHyY1lgothd38Gy2QVkZQR62l4kpSydVUBxbmZC7+OREeH9/s059+z4G8xsmnNu0Dm3IQZ1JRTnHPsau7hrTYXfpYjIOGlpxrULZ7D5WCvOOczM75ImLdJh3/+c4LbN0SwkkZ0620/3wAgrK3TSUCRorl1YSmPnAHVtfX6XckUuOZI2s1nAHCDHzNYBY/8MFeJNfQje9qQAKyo0Hy0SNNcvnAHA7461Ma80z+dqJu9y0x134J0srAS+MO72buAvY1RTwtnX2El6mrFEl8sSCZz5pXnMKszmd8daeeDqar/LmbRLhrRz7lvAt8zs3c65H8appoSzr7GLReX5ZGem+12KiFzAzLhu4YxzW5cm2rz05aY73u+c+y4wz8z+7MLvO+e+MMHDUs7ehq5zu26JSPBcu3AGP9rRwOEzPQn3F+/lThyOTeDkAwUTHIHix94dzV0DtPYMaj5aJMCuPTcvnXirDy833fHV8Me/jU85U+Ocexp4esOGDX8Yr9ccO2m4UjvfiQRWZXEuVSU5bD7WxoPXz/e7nEmJdDHLP5hZoZllmtkvzazFzN4f6+ISwb6GLgCWzQ7cHxYiMs7GeSVsq2tPuEtqRdonfbtzrgt4O97eHTXAJ2NVVCLZ29jJ/NI8bU8qEnCb5pXQ1jvE8dbEuqRWpCE9Ni3yNuAHzjl/NmwOoH2NXSzXfLRI4G2YVwLA1hNnfa5kciIN6WfM7CCwHvilmZUBA7ErKzF09A1R396vlYYiCWBhWR4leVm8XtvudymTEulWpZ8GrgM2OOeGgV7gnlgWlgj2N3rz0ersEAk+M2PD3GK21iXWSDrSDZYAluL1S49/zLejXE9C2aeQFkkom+aX8Pz+MzR3DVBemO13ORGJKKTN7DvAQmAnMHZVR0eKh/SBpi7KC6YxI3+a36WISAQ2huelt5xo522rZ/tcTWQiHUlvAJa7ROtdibGDp7tZOlujaJFEsbyikJzMdLacOJswIR3picO9wKxYFpJoRkZDHG3uYVmCLTEVSWWZ6WlcNXc6WxKowyPSkXQpsN/MXgcGx250zt0dk6oSQG1rL0OjIZZqEYtIQtkwt4R/+tURugeGE2J9Q6Qh/dlYFpGIDjR1A7BkpqY7RBLJpvklhBxsq2vn5iXlfpdzWZG24L2Et9IwM/z5FmB7DOsKvENNXWSkGQvLE28TcZFUtrZqOmkGO052+F1KRCLdu+MPgSeAr4ZvmgP8JFZFJYKDp7tZWJbPtAztIS2SSPKmZbB4ZgE7TyVRSAMfA64HugCcc0eA4P+dEEMHm7o1Hy2SoNZVT2fnqQ5CoeA3rEUa0oPOuaGxL8ILWoL/08VIZ/8wDR39Cbd5uIh41lUV09k/TG1b8DdbijSkXzKzv8S7IO1twA+Ap2NXVrAdPuOdNFw2SycNRRLR2urpAOxMgHnpSEP600ALsAf4CPAs8NexKmo8M3uHmf2bmT1mZrfH4zUv5+Bpbzm4pjtEElNNWT4F0zLYcSr4my1F2t0RwjtR+MfOuXudc/8WyepDM/uGmTWb2d4Lbr/TzA6Z2VEz+/RlXvsnzrk/BD4K3BdJvbF2oCIpqvkAABMySURBVKmbopxMZiXI2n8ReaO0NGN1VVFCdHhcMqTN81kzawUOAYfCV2X57xE+/zeBOy94znTgX4C3AMuB+81suZmtMrNnLjjGn5z86/DjfHeoqZslswoS7qrDInLeuqpiDjZ10z80evk7++hyI+lP4HV1bHTOlTjnSoCrgevN7BOXe3Ln3MvAhesvNwFHnXPHwycjvw/c45zb45x7+wVHc/gfiv8N/Mw553tvdijkONTUreXgIglubdV0RkOOPQ3BvobJ5UL6A8D9zrnasRucc8eB9wN/cIWvOQc4Ne7r+vBtF/MnwJuBe83soxe7k5k9ZGZbzWxrS0vLFZZ2eQ0d/fQMjmhjJZEEd+7kYcDnpS+3LDzTOfcfroHunGsxs7gsenfOfQn4UgT3ewR4BGDDhg0xaw88FF4OvnimRtIiiaw0fxrVJbmBn5e+3Eh66Aq/dykNQNW4ryvDtyWEI809ACyame9zJSIyVWurpid8SK8xs64Jjm5g1RW+5hZgkZnNN7Ms4H3AU1f4XG9gZneZ2SOdnbGbYzpypptZhdkUJsDuWSJyaeuqp9PUNUBTZ3Av2XrJkHbOpTvnCic4Cpxzl00pM/sesBlYYmb1ZvYh59wI8DDwc+AA8Lhzbl80fhjn3NPOuYeKimJ3YdgjzT0aRYskidWVXlYE+eThZK5xOGnOufsvcvuzeAtiEkoo5Dja3MMDV1f7XYqIRMHy2UWkGeyp7+C25TP9LmdCka44TAixnu6ob++nf3iUReUaSYskg5ysdBaVFwR6JJ1UIR3r6Y4jzV5nxyJ1dogkjZVzitjT0ElQL+GaVCEda4fPeJ0dNRpJiySN1ZVFtPYM0dQVzJOHCulJONLsdXYU5aizQyRZrJwTPnlYH8wpD4X0JBw5o84OkWSzfHahd/IwoPPSSRXSsTxxONbZsahc89EiySQnK53FM4N78jCpQjqWJw4bOsKdHRpJiySdlXOK2FMfzJOHSRXSsTR2NZbFCmmRpLO6soi23iFOB3DloUI6QmN7dtRoukMk6Zw7eRjAKY+kCulYzkkfPtPNzMJp6uwQSULLZxeSnmaB7PBIqpCO5Zz00eYebU8qkqSyM9NZVJ6vkXSiGuvsWFim+WiRZLVqThF7A7jyUCEdgaauAfqG1NkhksyWVxTS1jtES/eg36W8gUI6AsdavJOGC0oV0iLJaln4knj7T3f5XMkbKaQjcCzc2bGwPM/nSkQkVhTScRCr7o5jLb0UZGdQlj8tqs8rIsFRlJNJZXEO+xsV0jETq+6O4609LCjLx8yi+rwiEizLZhdyQCPpxHOsuZeFZZrqEEl2y2cXcry1l76hEb9LOUchfRk9gyM0dQ2o/U4kBSyvKMQ5ONTU7Xcp5yikL6O2pRdAIS2SApaHTx4eOK2QThhj7Xea7hBJfpXFORRMy2D/6eCsPFRIX8axlh7S04zqGbl+lyIiMWZmLKsoDFSHR1KFdCxa8I619FBdksu0jPSoPaeIBNfy2YUcbOomFArG8vCkCulYtOAdb+llQammOkRSxfLZhfQNjVJ3ts/vUoAkC+loGw05jrf2slBXBxdJGcsrwisPAzLloZC+hIb2foZGQjppKJJCasrzSU+zwJw8VEhfwvnODo2kRVJFdmY6C8vyAtMrrZC+hHO73ymkRVLK4pkFHFRIB9+xll6KczMpycvyuxQRiaOlswqob++nZ9D/5eEK6Us43tKjUbRIChq7VN6RM/6PppMqpKPdJ13b2st8td+JpJwls7yQDsK8dFKFdDT7pHsHR2juHlRIi6SgquJccjLTOaSRdHCdaPM2Vpo3QyEtkmrS0ozFM/M5rJAOrhOt3mqjeaXas0MkFS2eWaDpjiCrbfXa7zSSFklNS2YV0NozRGuPv1cPV0hfRG1rHzMLp5E3LcPvUkTEB2MnD/2e8lBIX8SJtl6NokVS2JKZwejwUEhfxAm134mktLKCaRTnZmokHUSd/cO09Q4xTyEtkrLMLBAnDxXSEzjR6rXfaSQtktqWzCrg8JkenPPvAgAK6QmM9UgrpEVS25JZBfQMjtDQ0e9bDQrpCdS29mIG1SXqkRZJZUE4eaiQnsCJ1l4qinLIztR1DUVS2aKxjZaae3yrIalCOlobLNW29WmqQ0QoysmkvGAaRxXS0RGNDZacc9S29Gg5uIgA3uW0NJIOkPa+YboGRrSQRUQAWFSez7Fm/zo8FNIXqFX7nYiMU1OeT8/gCE1dA768vkL6AuqRFpHxFpZ7V2fya15aIX2BE229pBlUFmtOWkRgUfnYpbQU0oFQ19ZHxfQcsjL01ogIlOZnUZSTydEWhXQg1J3tY+4MjaJFxGNmLCrP56hG0sFwsq2X6hLNR4vIeTXl+RpJB0HXwDDtfcPM00haRMapKc/nbO8QbT5cpUUhPc7JNu+6hpruEJHxanzs8FBIj1MXDmlNd4jIeH7u4aGQHqfurNcjXa2RtIiMU1GUTW5WukbSfjvZ1kdpfhb5uvisiIxjZt7JQ4W0v+ra+rSHtIhMqKZMIe27k2f7mKuNlURkAjUz82nqGqBrYDiur6uQDhscGaWxs18jaRGZ0MIyr8PjeEtvXF9XIR1W396Pc2q/E5GJLSzz/so+HudFLYEPaTNbZmZfMbMnzOyPYvU66pEWkUupLskjPc2SayRtZt8ws2Yz23vB7Xea2SEzO2pmn77UczjnDjjnPgq8F7g+VrWOXSFcPdIiMpGsjDSqinPO7TkfL7EeSX8TuHP8DWaWDvwL8BZgOXC/mS03s1Vm9swFR3n4MXcDPwWejVWhdW195GalU5qfFauXEJEEt6Asn2Nxnu6IaUOwc+5lM5t3wc2bgKPOueMAZvZ94B7n3OeAt1/keZ4CnjKznwKPTnQfM3sIeAigurp60rWePOu135nZpB8rIqlhfmkevzvWSijkSEuLT1b4MSc9Bzg17uv68G0TMrObzexLZvZVLjGSds494pzb4JzbUFZWNumi6tp6NR8tIpe0oCyPgeEQjZ39cXvNwC+tc879Gvh1LF8jFHKcau/n1mUzY/kyIpLgFpSeb8OL19Wb/BhJNwBV476uDN82ZWZ2l5k90tnZOanHNXUNMDQSUo+0iFySH214foT0FmCRmc03syzgfcBT0Xhi59zTzrmHioqKJvW4OrXfiUgEygqmkT8tg+Nx7PCIdQve94DNwBIzqzezDznnRoCHgZ8DB4DHnXP7YlnH5ayrns5P//QG1lUX+1mGiAScmbGgLC+ubXix7u64/yK3P0sM2+kmKzsznRUVkxt9i0hqWlCax5YT7XF7vcCvOJyMK52TFhGJ1IKyfBo6+ukfGo3L6yVVSF/pnLSISKQWhE8exmvKI6lCWkQk1uaXhjs8WuPT4aGQFhGZhHMhHaeNlpIqpDUnLSKxlpuVQUVRdtx6pZMqpDUnLSLxsKAsP2690kkV0iIi8TC/1OuVds7F/LUU0iIikzSvNI/ugRHO9g7F/LUU0iIikzS/1NtC4kR4S4lYSqqQ1olDEYmHuTO8Do8TcZiXTqqQ1olDEYmHquJc0uz8ZfdiKalCWkQkHrIy0phTnKPpDhGRoJo3I0/THSIiQTW/NI8TbbFvw0uqkNaJQxGJl7kz4tOGl1QhrROHIhIv59vwYjvlkVQhLSISL+fb8GJ78lAhLSJyBeLVhqeQFhG5AvFqw1NIi4hcoXi04SmkRUSu0PxSL6Rj2YaXVCGtFjwRiae5M/LoHoxtG15ShbRa8EQknuLRhpdUIS0iEk/xaMNTSIuIXKF4tOEppEVErtBYG15tDDs8FNIiIlMwtySPU2c13SEiEkjVM3I5qZAWEQmm6pJc2vuG6RoYjsnzK6RFRKZgbonXhncyRsvDkyqktZhFROKtaiykYzTlkVQhrcUsIhJv1TMU0iIigVWYnUlxbiZ1mu4QEQmm6hmxa8NTSIuITFF1SS51Z2OzoEUhLSIyRXNLcmnsGGB4NBT151ZIi4hMUXVJLqMhR2NHf9SfWyEtIjJFsezwUEiLiExRdbhXOhYdHgppEZEpmlWYTVZ6Wkw6PBTSIiJTlJZmVJbkaCQtIhJUc0tisxteUoW09u4QEb9Uh0M62lcOT6qQ1t4dIuKX6hl59AyO0N4X3S1LkyqkRUT8cr7DI7orDxXSIiJRMDdGvdIKaRGRKKgqzuX+TVVUFudE9XkzovpsIiIpKicrnc+9a3XUn1cjaRGRAFNIi4gEmEJaRCTAFNIiIgGmkBYRCTCFtIhIgCmkRUQCTCEtIhJgCmkRkQBTSIuIBJhCWkQkwBTSIiIBZtG+ikAQmFkLUHfBzaVAqw/lTEbQa1R9UxP0+iD4NSZrfa3OuTsn+kZShvREzGyrc26D33VcStBrVH1TE/T6IPg1pmJ9mu4QEQkwhbSISIClUkg/4ncBEQh6japvaoJeHwS/xpSrL2XmpEVEElEqjaRFRBKOQlpEJMCSLqTN7E4zO2RmR83s0xN8/4Nm1mJmO8PHh+Nc3zfMrNnM9l7k+2ZmXwrXv9vMrgpYfTebWee49++/x7m+KjN70cz2m9k+M/v4BPfx7T2MsD6/38NsM3vdzHaFa/zbCe4zzcweC7+Hr5nZvIDV5+vvcbiGdDPbYWbPTPC96L1/zrmkOYB04BiwAMgCdgHLL7jPB4F/9rHGG4GrgL0X+f5bgZ8BBlwDvBaw+m4GnvHx/ZsNXBX+vAA4PMF/Y9/ewwjr8/s9NCA//Hkm8BpwzQX3+WPgK+HP3wc8FrD6fP09DtfwZ8CjE/23jOb7l2wj6U3AUefccefcEPB94B6fa3oD59zLwNlL3OUe4NvO8yow3cxmx6e6iOrzlXPutHNue/jzbuAAMOeCu/n2HkZYn6/C70tP+MvM8HFhB8E9wLfCnz8B3GpmFqD6fGVmlcDbgK9d5C5Re/+SLaTnAKfGfV3PxL8g7w7/GfyEmVXFp7SIRfoz+Ona8J+iPzOzFX4VEf4Tch3eSGu8QLyHl6gPfH4Pw3+q7wSagReccxd9D51zI0AnMCNA9YG/v8f/F/gUELrI96P2/iVbSEfiaWCec2418ALn/7WTyGwH5jrn1gD/BPzEjyLMLB/4IfBfnHNdftRwKZepz/f30Dk36pxbC1QCm8xsZbxruJQI6vPt99jM3g40O+e2xeP1ki2kG4Dx/6JWhm87xznX5pwbDH/5NWB9nGqL1GV/Bj8557rG/hR1zj0LZJpZaTxrMLNMvAD8d+fcjya4i6/v4eXqC8J7OK6WDuBF4MLNfc69h2aWARQBbfGt7uL1+fx7fD1wt5mdwJtS/T0z++4F94na+5dsIb0FWGRm880sC2/C/qnxd7hgbvJuvDnDIHkK+INwh8I1QKdz7rTfRY0xs1ljc2tmtgnv/6G4/fKGX/vrwAHn3Bcucjff3sNI6gvAe1hmZtPDn+cAtwEHL7jbU8B/Cn9+L/ArFz4LFoT6/Pw9ds59xjlX6Zybh5cxv3LOvf+Cu0Xt/cu44koDyDk3YmYPAz/H6/T4hnNun5n9D2Crc+4p4E/N7G5gBO8E2QfjWaOZfQ/v7H6pmdUDf4N3YgTn3FeAZ/G6E44CfcCDAavvXuCPzGwE6AfeF69f3rDrgQ8Ae8JzlgB/CVSPq9HP9zCS+vx+D2cD3zKzdLx/IB53zj1zwe/J14HvmNlRvN+T9wWsPl9/jycSq/dPy8JFRAIs2aY7RESSikJaRCTAFNIiIgGmkBYRCTCFtIhIgCmkJWmYWc/l7+U/M/usmf2F33VIYlBIi4gEmEJakk54peHnzWyvme0xs/vCt6eZ2ZfN7KCZvWBmz5rZveHv/b15e0DvNrP/E77trvBewDvM7BdmNjN8+2fN7Ftm9hszqzOzd5nZP4Rf67nwsnDM7MS42183s5oJal0Yfsy28PMtjd87JYlAIS3J6F3AWmAN8Gbg8+FlxO8C5gHL8VYFXgtgZjOAdwIrwhv2/M/w87yCt4/xOrw9Gj417jUWAr+HtyT5u8CLzrlVeCsI3zbufp3h2/8Zb+e0Cz0C/Ilzbj3wF8CXp/STS9JJqmXhImE3AN9zzo0CZ8zsJWBj+PYfOOdCQJOZvRi+fycwAHzdvKtsjF1poxJ4LBzwWUDtuNf4mXNu2Mz24G1B8Fz49j14/xCM+d64j18cX2R4p7zrgB/Y+a2Gp13xTy1JSSNpSXnh/X434W3O/nbOB+4/4V39YxXwESB73MMGw48NAcPj9t4I8cbBj7vI5+D9/nU459aOO5ZF42eS5KGQlmT0G+C+8MbxZXiXBHsd+C3eRvFp4fnlm+HciLYovG3oJ/CmScDbXnJsi9P/xJW5b9zHzeO/Ed5nutbM3hOuw8xsDSLjaLpDktGP8eabd+GNXj/lnGsysx8CtwL78a6asR1vqqMAeNLMsvGur/dn4ef5LN5URDvwK2D+FdRSbGa78Ube90/w/d8H/tXM/hpvt8Hvh+sWAbQLnqQYM8t3zvWETxa+DlzvnGuK0WudADY451pj8fySGjSSllTzTHhD+Szg72IV0CLRopG0iEiA6cShiEiAKaRFRAJMIS0iEmAKaRGRAFNIi4gE2P8PrVWHVaWlRoAAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"source": [
"# bounded rejection sample\n",
"\n"
],
"metadata": {
"id": "_QJy0JrQwi9d"
}
},
{
"cell_type": "code",
"source": [
"lower_bound, upper_bound = 3.0, 10.0"
],
"metadata": {
"id": "OxT9s-4Bwi9e"
},
"execution_count": null,
"outputs": []
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from bounded rejection sampling\n",
" data = pd.DataFrame.from_records([{\n",
" 'sample' : bounded_pareto_rejection_sample(alpha=alpha, lower_bound=lower_bound, upper_bound=upper_bound),\n",
" } for __ in range(10000)])\n",
" sns.displot(data=data, x='sample', kind='ecdf')\n",
"\n",
" #expected\n",
" x = np.geomspace(data['sample'].min(), data['sample'].max(), 100)\n",
" plt.gca().plot(x, bounded_pareto_cdf(x, alpha=alpha, lower_bound=lower_bound, upper_bound=upper_bound),'r-', lw=5, alpha=0.6)\n",
"\n",
" plt.gca().set(xscale=\"log\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"outputId": "cf98df08-05de-409f-c86e-ff364a4ef5ca",
"id": "hOiuCEx8wi9e"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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6VpbmV7KDvvD1b/LtK05W+MYpBbCIH5yD557zPtqbvP7eVdtqqBk4iFm/upP5xx7mY5ESbQpgkZ4WDsOjj8Jbb7U3tYXCvJtbQUltC27SIVz+l58xaPgg/2qUHqEAFulJwaA3waLDeibBkOONDWVUNbQxen42J/76DpL7pflYpPQUBbBIT2lt9dbxzclpbwqGHK9tKPXC96xTWPDTWyFZWwclCgWwSE9oaoI//hHy89ubKhtaWV5QTVVDG8MuPo8F3/tv0M22hKIAFom2ujr4/e+9nYsjKhtaeWVdKc7BuOuv4sQbr/SxQPGLAlgkmior4f/+D8o+2WWruKaZ9/IqSE3pw/E/+gYjzzrVxwLFTwpgkWgpLYXf/Q6qqwFvmNnqolrWba/DJScz7+ffZeTp830uUvykABaJhqIi78q3vr69aWf4jhyeybxf30HG7Jk+Fii9gQJYpLvl53s33Jqa2ps+LvbCd8ToIZxy10+wQw7xsUDpLRTAIt1p0yb405+8IWcRa4pqWVtcy5DRQznpr/+LjRvrY4HSmyiARbpLTo63kHqHjTMLq5pYu72WPsOHsuDeX5EyWptmyicUwCLdYfVquOeeTiualde3smRzJTZiBKf/7Rekjh7pY4HSG2kzKZGDtWIF/OUvncK3oqGVxbnlVA8ezoJ7fsngcQpf+TRdAYscjGXLvLUdIstJOudYu72Oj4trqRk+mtPv/hmjxo/wuUjprRTAIgdqyRL45z/bwzfkHMvyq9ha0UjtmPF89r5fMHqkVjSTPVMAixyId96BBx9sPwyFHUs2V1BY1czgY2Zx+V0/wtK0opnsnQJYZH+99RY8/HCnpg+3VVNY1czw447m9D/8EFJSfClNYosCWGR/vPkmPPJI+6FzjpUF1eSWNpAx5yhO/+OPoI9+rKRr9J0i0lW7hG8w7Hgnt5wdNS2kzDmas//0A4Wv7Bd9t4h0xS7h2xYKs3hTOWV1rYw67QQW/PI2TOEr+0nfMSL7spsr3zc3lFHZ2MbkcxYw7yffhiQNqZf9pwAW2Ztdwrc1GObtTeVUNrQx+dxTmPfjbyl85YApgEX25O23P9Xt8NbGMqoa2zj0vFOZ+6NbFb5yUBTAIrvzzjvw73+3HwbDjjfWe+E75fzTmPPDbyp85aApgEV2tWRJp0kWbaEwb27wwnfSOacofKXbKIBFOlq2zJteHBEIhXl9fSnVTQEmnb2AY3+iPl/pPgpgkZ1Wruy0sE4w7Hg3r4LqxgBTzjqZOT/VaAfpXvpuEgFvPd977+20qtnyLVXsqGlh1ILjFL4SFboCFsnJ8RZTD4cBr9thaX4lRVXNZM47hlN+8z+QnOxzkRKPFMCS2DZt8rYRiiymHgiFeX1DGVUNbYw7MZv5v71T04slavSdJYkrP9/bQDOyh1sw7HhrYzlVjW3MPG0eM39xh1Y1k6hSp5YkpsJCb+v4yO7Fzjnez6+kvL6VQ487kpk/v13hK1GnAJbEU1ICv/89NDW1N31cXMe2yiaGz5rG3N/+AFJTfSxQEoW6ICSxVFbC734H9fXtTSsKqtlUUk/65AmcctdPQTtZSA9RAEviqK31wrempr1pU2k9m0rqGTBhDGfe+0uSB/T3sUBJNApgSQyNjV63Q3l5e1NeWQMrtlaTNnIYC+/7JSmDMn0sUBKRAljiX2urN9qhuLi9Kbe0nuVbq8kYPpjP3PdLUoYO8bFASVQKYIlvwaA3zjc/v72pvL6V5VurGTg0k5Pu/jnpY0b5WKAkMo2CkPgVDsP998P69e1NDa1BFueW41L7Mu93P2Lg5Ak+FiiJTgEs8ck5b+v4lSvbmxpbg7y6rpQWZ8z79Z0MmznNxwJFFMASrxYtgsWL2w93hm9z0DH5f77JoScd42NxIh71AUv8eeMNeOGF9sPy+lbeyS2nLRhm+u1fY/ZFp/pYnMgnonoFbGYLzWyjmeWZ2W17OOdSM1tnZjlm9u/dnSPSZcuXw6OPth82tgZ5a2MZSWYcdev1zL70LB+LE+ksalfAZpYM3AV8BigClpvZIufcug7nTAFuB05wzlWb2fBo1SMJYP16b0H1iGDIW1A9EHYce+MVjLvqIh+LE/m0aF4BzwXynHP5zrk24BHggl3OuR64yzlXDeCcK4tiPRLPCgq84WahUHvT6qIab/v4C85g3LWX+1icyO5FM4DHAIUdjosibR1NBaaa2Xtm9r6ZLdzdE5nZDWa2wsxWlHeYySQCQFlZp5XNALZVNbGxpJ60OUcz785bwMzHAkV2z+9REH2AKcAC4HLgb2aWtetJzrl7nHPZzrnsYcOG9XCJ0qvV18Mf/tBpcZ0dtc28m1tB3biJnPm772krIem1ovmdWQyM63A8NtLWURGwyDkXcM5tATbhBbLIvrW2ele+Hf4qag6EeC+vkoahw7nobz8jo38/HwsU2btoBvByYIqZHWJmfYHLgEW7nPM03tUvZjYUr0siH5F9CYW8fdwKCtqbWoNhlmyuoCwlneN//2OGjxzsY4Ei+xa1AHbOBYGbgJeB9cBjzrkcM/uxmZ0fOe1loNLM1gFvAt92zlVGqyaJE87BQw/B2rXtTcGw4728CrY0QdZt32bGdE0xlt7PXGQb7liRnZ3tVqxY4XcZ4qfnn/dmunWwOLecLbVtpH7rVi67/BSfChPZo93eBdbdCYktS5Z8KnyXb62isLqZ0LXXKXwlpiiAJXasXw//+lenppLaFnJLG6g572K++NXP+lSYyIHp8kw4MzsemNjxc5xz/4xCTSKfVlwMf/mLt8RkRF1zgHdyy1k/61huu+MakpM01ldiS5cC2Mz+BUwGPgJ2TjVygAJYoq+mxhtu1tLS3tTYGuS19WWsHzuN6/7frWSkal0piT1d/a7NBo5wsXbHTmJfS4u3nVB1dXtTMOR4Y0MZ6waM4PRffZeJw7SRpsSmrvYBrwVGRrMQkU8Jh+Fvf4PCT2a0O+d4J6+c/OQBHPXz/+H4afq2lNjV1SvgocA6M/sAaJ9w75w7f8+fInIQnPOWleww1hdgRUE1uU1Gyne+xjnHTvapOJHu0dUA/mE0ixD5lDfegLfe6tT0cXEt6yqaKbr6K/zo4nn+1CXSjboUwM65t81sBDAn0vSBlo6UqPn4Y3j88U5NBZWNrCmuZdP5V/CDG8/GtLqZxIEu9QGb2aXAB8DngEuBZWZ2STQLkwRVVOT1+3a439vQGmTZlio+nHMad9xxOX37aPi6xIeudkHcAczZedVrZsOA14AnolWYJKDaWm/EQ4d1fQOhMO/lVfDemOnc/JP/Ir2vhptJ/OjqpUTSLl0OlfvxuSL7FgjAn//cabhZKOxYnFvO0rSRHH/HjRw6YoCPBYp0v65eTrxkZi8DD0eOPw+8sJfzRbrOOfj732Hr1g5N3n5ua0IZTPj+LXx+3kS/qhOJmq7ehPu2mV0MnBBpusc595/olSUJ5bnnYJcV7lZuq2FjI/T59k1ce/oRPhUmEl1d7lBzzj0JPBnFWiQRrVjhBXAHWysbWV/eRMEVX+anlxzrU2Ei0bfXflwzezfy33ozq+vwUW9mdT1TosStggKv66GDqsY2luRV8sH8c/jWVzTcTOLbXq+AnXPzI//V3Q/pXjU13k23QKC9qbY5wOJN5SyZNpc7f3ItgzL6+ligSPR1dRzwv7rSJtIlgQDcfbcXwhF1LQFeW1/KmuGTuOrnNzN8YJqPBYr0jK72AU/veGBmfYBjur8ciXvOeYuqdxjxEHaOd3Mr2DFgGBf9/nvMmDzUv/pEetC++oBvN7N6YFbH/l+gFHimRyqU+PLqq7BsWaemnO11FIZSGP+9W5kxebhPhYn0vL0GsHPuf4FM4J/OuYGRjwHOuSHOudt7pkSJG2vXwlNPdWoqqW3hox0N5F10FecumOFTYSL+2GcXhHMubGZz9nWeyF6VlsK993Za46GqsY03N5bx5tyz+O3N55CkLYUkwXR1OvGHCmE5YC0t3oiH5ub2pobWIG9vKmfNYdn8+BdfJitdIx4k8XT1Jtw84EozKwAa8fa4d865WVGrTOKDc3DffVBS0t4UCjve3FBGTtYYLv7ZLYwdlO5jgSL+6WoAnxnVKiR+PfssrFnTfhh2jmVbqtiSlMHcn32H7Eka8SCJq0tdEM65AiALOC/ykRVpE9mzjz6C55/v1LRqWw0ba9oIXP9fnDFHWwpJYuvqRIxbgIeA4ZGPB83s5mgWJjFuxw64//5OTfnljWwsqafsc1dy67Wn+FSYSO/R1S6I64B5zrlGADP7JbAU+GO0CpMY1tzszXTrsLD6tqom3t9SSd6xC/jWNy72sTiR3qOroyAMCHU4DkXaRDpzDh54wBt2FlHV2MaSzZWUTpzGTb/5una1EIno6k/CA3j7wP0HL3gvAO6LWlUSu154AVavbj+sbQ7wyrpSagcO4uI/3cng/qk+FifSu3R1QfbfmtlbwHzAAdc651ZFszCJQWvXeqMeIsobWnk1p5RA374s+L8fMH7MYB+LE+l99vdvQcMLYHU/SGcVFd5438hMt9rmAO/mVpCWksT073+DaUdO9blAkd6nq6Mg7gT+AQwChgIPmNn3olmYxJC2Nu+mW1MT4PX5vpxTQjAUZvZ/XcHs8xb4W59IL9XVK+ArgdnOuRYAM/sF8BHw02gVJjHCOXjoISgqAqC+JcBbG8sx4KQLFzDiS5f7W59IL9bVURDbgY4rZKcCxd1fjsScd96B998HvFlub2+qoDUYYsHxhzPiGzdCUle/xUQST1evgGuBHDN7Fa8P+DPAB2b2BwDn3NeiVJ/0Zlu3wqOPth9uLKmnrjnA3KkjGPadr0NGhn+1icSArgbwfyIfO73V/aVITGlshL/+FYJBAJoDIT4qrGFEZiqTb7kexo3zuUCR3q+rw9D+YWZ9gZ23sjc65wJ7+xyJY85504yrqtqbPi6qxQHTLz0HO+EE/2oTiSFdCmAzW4A3CmIr3hC0cWb2Refc4uiVJr3WCy94Y34jCiqbyCtrYNiMqYy84Rr/6hKJMV3tgvh/wBnOuY0AZjYVeBhtzJl4NmzoNNmiJRBi2ZZKUjP7c+Jv7oCUFB+LE4ktXb1FnbIzfAGcc5sA/aQlmpqaT20rtLKgmmDIcdjtt5A2UhtqiuyPrl4BrzSze4EHI8dXAiuiU5L0SuGwF7719e1NeWUNFFQ2kXr+uUxfON/H4kRiU1cD+CvAjcDO4WbvAH+OSkXSOz3zDOTmth9WNrayYms1gUOncMn3/svHwkRi1z4D2MySgdXOucOA30a/JOl11q6Fl15qP2xsDfL2xnLaMjI47w/fp6+WlxQ5IPvsA3bOhYCNZja+B+qR3qa6utPOFsGQ473NlbSFHPN+fhuDRw/zsTiR2NbVS5dBeDPhPsDbFRkA59z5UalKeodQCP72N2/SBeCc473NFVTUtzL+S1cw7SQNghE5GF0N4O9HtQrpnRYtgs2bAS98l+RXUlzdzOC5RzH/5qt8Lk4k9u01gM0sDe8G3KHAx8B9zrlgTxQmPsvJ6dTvm1/RSEFFEyMnjGTBr28D05LQIgdrX33A/wCy8cL3LLwJGRLvamq8fd0i6lsCrNhazaABqcz/xW0kZQ70sTiR+LGvLogjnHMzAczsPuCD6JckvgqHvZ0tIuN9nXMs21JFksHcr11D38On+VygSPzY1xVw+4I76npIEC++CJs2tR9+VFhDWV0r4044hiGXXOBjYSLxZ18BPNvM6iIf9cCsnf82s7p9PbmZLTSzjWaWZ2a37eW8i83MmVn2/n4B0o1yc9vXeXDO8W5eBet31DN09DDm/Phb6vcV6WZ77YJwziUf6BNHJnDchbd4exGw3MwWOefW7XLeAOAWYNmBvpZ0g8bGTptqbi5vZFtlE+OGZHD8b24nOSvT5wJF4k8094uZC+Q55/Kdc23AI8Du/ob9CfBLoCWKtcjeOAf/+Ic36QJoaA2yals1WekpHHvjlSQfcbjPBYrEp2gG8BigsMNxUaStnZkdDYxzzj0fxTpkX95+G1avBiKTLfIqCIVhzmlzSPms+n1FosW3HRPNLAlvbYlbu3DuDWa2wsxWlJeXR7+4RFJcDI8/3n64oaSeyoY2Zk0bxTBtqikSVdH86beNVHYAABZESURBVCoGOm4MNpbOOykPAGYAb5nZVuBYYNHubsQ55+5xzmU757KHDdPaA92mrc1bYjKyr1sgFGZtcS0jM9M47Ns3wuDBPhcoEt+iGcDLgSlmdkhkP7nLgEU7H3TO1TrnhjrnJjrnJgLvA+c757TOcE954gnYvr39MLesgUDIMfaCM0k65mgfCxNJDFEL4Mi44ZuAl4H1wGPOuRwz+7GZaREfv61e7fX9RuyobeajwhrCo0Yx+cYv+ViYSOKI6kKuzrkXgBd2abtzD+cuiGYt0kFNjTfqIaK+JcC7uRWkp6dy8u+/R3JqXx+LE0kcusOSaJyDv/+90xKTy7ZUEQg5Zn/9ywyaOsnf+kQSiAI40bz+Oqxf3364pqiWsrpWxp48j0MuOcfHwkQSjwI4kRQVwX/+035Y2xxg3Y46MkcO4cSffFNTjUV6mAI4UQQCnYacAawuqiE5yZj7w29gA7XEpEhPUwAniiefhB072g8Lq5soqmom5YzTGXasthYS8YMCOBHk5MCbb7YfVja2sXRzJYGRozjze//tY2EiiU0BHO8aGzsNOQuFHW9vLKfFJXHiL75LekY/H4sTSWwK4HjmHDz4INTWtjetLqqhJRDi8Bu/yKQjtbuFiJ8UwPFs2TL48MP2ww0l9WzYUU/fmUeQfe3FPhYmIhDlmXDio8pKePjh9sOqxjY+2lZN/8EDOft3/4NplTMR3+mnMB7tnO3W4q1x39Aa5O1N5fRJTuKkH95Cn6FD/K1PRAAFcHx6/fX2jTWdc3ywpYrWYJhjLl1I1knH+1yciOykAI4327d3mu1WWN1MSW0Lhx0+jkNuus7HwkRkVwrgeBIKwQMPtM92awuFWVlQTUZqMoff9jVIT/e5QBHpSAEcT154AbZtA7yuh8WbymluC3HYFReQOnO6z8WJyK4UwPGioMAL4Ii88kbK6lqZOvtQpn31Gv/qEpE9UgDHg0DA63oIhwGoaQqwcmsVQwemcdQPvgkpKT4XKCK7owCOB4sWtS+045zjw23VJCUZ2f99BcmTDvG5OBHZEwVwrNu8GV59tf1w5bYaSmpbGDNzKoM/d6GPhYnIviiAY1lbmzfhwjkAyhta2VRSz5ihAzj+p9+CPproKNKbKYBj2dNPQ1kZAIHIkLPUlCSyv3Y1Nnasz8WJyL4ogGNVbi688Ub74Qdbq6hqaOOI42eTce7ZPhYmIl2lAI5Fra3eGr+RrofimmYKKpo4bPxgDr/9a6CFdkRign5SY9Ezz0B5OQA1zQGWbq4kvW8yM776BRg50ufiRKSrFMCxpkPXQyAUZunmCsxg/sJ59D3jDJ+LE5H9oQCOJW1t8M9/tnc9rCmqpboxwJwpIxh64w3qehCJMfqJjSXPPNM+6qG5LURuWQPjh6Qz/ktXwIgRPhcnIvtLARwr8vO9dX4j1hTXEHaOaccfCaee6mNhInKgFMCxIBDoNOqhqLqZzWWNHDp6EMNuUteDSKzST24seO45KCkBIBh2rCyoIiM1mVlf/YK6HkRimAK4t9u2DV55BYCwcyzdXEFja4gZJ8wm7awzfS5ORA6GArg3C4W8UQ+RZSZzttdRWNXMrAmDmfytG9X1IBLj9BPcm73yChQWAlBW38rHxbWMHdSP6ddfDqNH+1yciBwsBXBvVVLi9f0CoUjXQ0bfZOaeOAtbuNDn4kSkOyiAeyPnvK6HyOaaOcV1NLaGOGrCYNKuu1bLTIrECQVwb7R4sbfQOlBe38ra4lrGDu7HuM9fABMm+FyciHQXBXBvU10NTz0FQCjsWLalkrSUJObOPQw7/3yfixOR7qQA7k2cg3//G1paANhUWk9dc5BjJgwi7dovanNNkTijAO5NVq6ENWsAb2fjjwprGJGZyvjzz4Bp03wuTkS6mwK4t2hqgkcfBbydjT/YUklykjFv9iHYJZf4XJyIRIMCuLd46imoqwOgqKaZioY2Zo7JpP+1V0N6us/FiUg0KIB7g9xceOcdAFoCIVYWVJORmszUM+fDUUf5XJyIRIsC2G/BIPzrX+2HHxfX0tQaYu7hY0i+4gofCxORaFMA++2ll6C0FIAdtc3kljYwcWgGo665HAYN8rk4EYkmBbCfSkrgxRcBaA2GeC+vkv6pfcg+9Rg46SSfixORaFMA+8U5eOghCAZxzvFObgVtwTDHThlK3y9erZXORBKAfsr9snQpbNoEQH5FI2V1rcwel8nwi8+HMWN8Lk5EeoIC2A8NDfDEE4C3tfyaoloy+6VwxMxJcM45PhcnIj1FAeyHJ5+ExkYANpTU09wW4ugJg7Arr4S+fX0uTkR6igK4p+XmwpIlAFQ3tZGzvY7RWf0YdfqJMH26z8WJSE9SAPekYNC78YY33XjVthpwcMxho+DSS30uTkR6mgK4J736KuzYAUBJXQsltS3MHJvJgMsvhYEDfS5ORHpaVAPYzBaa2UYzyzOz23bz+DfNbJ2ZrTGz180sflcbr6iA558HvK3ll2+tJjUlianHztSYX5EEFbUANrNk4C7gLOAI4HIzO2KX01YB2c65WcATwK+iVY/vHn0UAgEAPi6uoaElSPbEIaRc/QUw87k4EfFDNK+A5wJ5zrl851wb8AhwQccTnHNvOueaIofvA2OjWI9/Vq9uX+e3tK6F9dvrGTOoH+M/dy6MG+dzcSLil2gG8BigsMNxUaRtT64DXtzdA2Z2g5mtMLMV5eXl3VhiD2hthUceAbwthlZsrSYtJYljj56kLYZEElyvuAlnZlcB2cCvd/e4c+4e51y2cy572LBhPVvcwXrhBaiqAmD9jjpqmwMcPWEQqVdcDmlpPhcnIn6K5v7mxUDHv6/HRto6MbPTgTuAk51zrVGsp+eVlHgjH4CKBm9349FZaUw8cQ4cfbTPxYmI36J5BbwcmGJmh5hZX+AyYFHHE8zsKOCvwPnOubIo1tLznIOHH4ZQiJZAiPfyKkhOMuZOGQGXX64bbyISvQB2zgWBm4CXgfXAY865HDP7sZnt7Pz8NdAfeNzMPjKzRXt4utizciVs2IBzjg+31dDYGuKEKUNJP+9sGD7c7+pEpBeIZhcEzrkXgBd2abuzw79Pj+br+6alBR5/HIC88ga2VjQybeQARk8eB2ed5XNxItJb9IqbcHHn+eehpobGtiCrttUwpH9fjh6fBZ//PKSk+F2diPQSCuDutmMHvPYazjmWb6kmHHbMmzQEmz0bZs3yuzoR6UUUwN3JOW/MbzhMfkUj22uamT4mk6yB6d7Vr4hIBwrg7rRqFWzYQGNrkJUF1Qzu35fpowfCwoUwdKjf1YlIL6MA7i6trfDYYwB8VFhDMOw4btIQkoYNgzPP9Lk4EemNFMDd5aWXoLqa4upmCiqbmDK8P5n9UnTjTUT2SAHcHSoq4JVXcM6xuqiG9L7JzB6XBTNn6sabiOyRArg7PPYYBINsqWiipinA4aMH0je1r3a5EJG9UgAfrJwcWL2a5rYQqwqrGdivD1OG94fPfEYz3kRkrxTAByMYhEcfxTnHsi2VtAXDzJs0hKRBgzTjTUT2SQF8MN58E0pLyStrYHtNC0eOy2JY/1S45BJITfW7OhHp5RTAB6quDp57juZAiFWFNQwbkMq0kQNgyhTIzva7OhGJAQrgA/X009DS4o35DTmyJwwiKSkJLrtMS02KSJcogA9EQQEsWUJ9S4At5Y1MGpbBoIy+cOKJMDY+t7UTke6nAN5fznk7HDvH+h31mMGssVmQng4XXLDvzxcRiVAA768VK2DzZhpag2wub2DSsAzS+ybD+edD//5+VyciMUQBvD/a2uDJJwHI2V4HwIzRmTBqFJx8sp+ViUgMUgDvj5dfhupqmtpCbK1o5JChGWSk9vHWe0jSWyki+0ep0VXV1V4A420vH3KOw0cN9NZ6OPxwn4sTkVikAO6qp56CQIC6lgC5pfVMHJJOZv80+Nzn/K5MRGKUArgrtmyBDz4AYN32OsyMo8YNglNP1XoPInLAFMD74lz7Qus1zQHyK7xxv/2GZME55/hcnIjEMgXwvqxYAfn5OOf4YEsVKUnG9NGZ3rCzfv38rk5EYpgCeG8CAa/vF2/YWUV9KzPHZpE+cRzMn+9zcSIS6xTAe/Paa1BVRXMgxNriWoYPTOWwkQO8hdY17ExEDpJSZE/q6uDFFwHvxlsYyJ442NtmSMPORKQbKID3ZNEiaG2lNRAit7SBQ4ZkkJURWetXRKQbKIB3p7gY3n0X8Pp+w855XQ8nnwwjR/pcnIjECwXw7jzxBDhHVWMbG0rrveUmh2bCuef6XZmIxBEF8K5ycmDdOsLO8cHWKvomJ3lbzJ99tlY7E5FupQDuKBz2rn6BLRWNVDW0cdT4LPqNGuHNehMR6UYK4I6WLoXt2wmEwqzaVkNWegqThmbAhRdCnz5+VycicUYBvFNrKzzzDACri2ppC4Y5evwgbPJkOOYYn4sTkXikAN7p1Vehtpby+lY2ldYzfkg6IzPTvGFn2mRTRKJAAQzepItXXiHkHO/nV5LWJ5k5EwfB0UfD5Ml+VycicUoBDPDss9DaSn5ZA/UtQY6ZkEVqal+v71dEJEoUwCUl8O67NLQGWVVYw+D+fRk/ON2bdKG1fkUkihTATz0F4TA522sJhh3HTRqC9euntX5FJOoSO4Dz8mD1ahpbg2wpb2TC4HQy+6XAWWdp0oWIRF3iBrBz8OSTOOdYta0GB8wcmwmDBsFpp/ldnYgkgMQN4I8+gvx88soa2FbVxLQRAxiYluLtdJGS4nd1IpIAEjOAw2H4z39obguxpriWwf37ctT4LBgzBo491u/qRCRBJGYAv/celJaypqiGtmCYORMGYWZw0UXa6UJEekzipU1rKzz7LJWNbWyuaOTQ4f0Z0j8Vpk6F6dP9rk5EEkjiBfAbb0BtLR8X1ZCSZMwam+W1X3yxphyLSI9KrABubISXXqKxNciO2hYOHd6f1D5J3pTjiRP9rk5EEkxiBfBLL0FLC6sKazAzDh0+wOvz/exn/a5MRBJQ4gRwdTW88QY1TQG2VTVx6PD+DEjrA/Pnw4gRflcnIgkocQL42WchGGRFQRV9kowZowd643015VhEfJIYAbxjByxZQlF1M2V1rcwck0laSjKcfjpkZfldnYgkqMQI4EWLCIfDrNpWzYC0PkwdMQDS0+GMM/yuTEQSWPwH8Nat8OGH5EXW+p0xJpPkJPMW3ElP97s6EUlgUQ1gM1toZhvNLM/MbtvN46lm9mjk8WVmNrHbi3j6aQKhMGuKahk6IJWJQ9K9bodTTun2lxIR2R9RC2AzSwbuAs4CjgAuN7MjdjntOqDaOXco8Dvgl91axIYNsH49xTXNtAXDzByT6U05PvdcLbgjIr6L5l7rc4E851w+gJk9AlwArOtwzgXADyP/fgL4k5mZc87t6UlzSxs483eLcXxySsezXYfGy15/iJHVJdQ1B0lPTWbkwFRvl4vjjz/oL05E5GDZXrLu4J7Y7BJgoXPuy5HjLwDznHM3dThnbeScosjx5sg5Fbs81w3ADZHDacDGAygpE6g9gM+LJ/H0HsTK19Kb6vSrlp583Wi/1lCgYp9nfVqFc27hro3RvALuNs65e4B7DuY5zOwe59wN+z4zfsXTexArX0tvqtOvWnrydaP9Wma2wjmX3V3PF82bcMXAuA7HYyNtuz3HzPrg/faqjFI9z0bpeWNJPL0HsfK19KY6/aqlJ1+3N73f+xTNLog+wCbgNLygXQ5c4ZzL6XDOjcBM59xXzOwy4CLn3KVRKUhE5CB19xVw1LognHNBM7sJeBlIBu53zuWY2Y+BFc65RcB9wL/MLA+oAi6LVj0iIt3goLpCdxW1K2AREdm7+J8JJyLSSymARUR8EhPD0PxiZhnAn4E24C3n3EM+l+QLvQ89S+934uj1V8BmlmZmH5jZajPLMbMfHcRz3W9mZZEJILs+trt1Ky4CnnDOXQ+cf6Cv253MLNnMVpnZcwfxHDH/PvQEM8sysyfMbIOZrTez4w7wefR+xykzm2Rm95nZEwfy+b0+gIFW4FTn3GzgSGChmR3b8QQzG25mA3ZpO3Q3z/V34FOzUfaybsVYoDByWuggv47ucguwfncPJNj70BN+D7zknDsMmM0u77ve7/i0p1+Yu/tl6ZzLd85dd6Cv1esD2HkaIocpkY9dh26cDDxtZqkAZnY98MfdPNdivOFuu2pft8I51wbsXLeiCO+HAXrBe2VmY4FzgHv3cEpCvA89wcwygZPwhkrinGtzztXscpre7/j0d3b5hdnFxcX2W0z8z4382f0RUAa86pxb1vFx59zjeOONHzWzK4EvAZ/bj5cYwydXHOD9AIwBngIuNrO76R0zbP4P+A4Q3t2DCfQ+9IRDgHLggUiXz72Rvtl2er/j0x5+Ye7pl+VBiYkAds6FnHNH4l0VzDWzGbs551dAC3A3cH6Hq+aDed1G59y1zrn/9vtGiJmdC5Q551bu7bx4fx96UB/gaOBu59xRQCPwqTWt9X4njN3+sjSzIWb2F+AoM7t9f580JgJ4p8ifgG+y+/60E4EZwH+AH+znU3dl3Qq/nQCcb2Zb8X77nmpmD+56UgK8Dz2lCCjq8NfWE3iB3Ine78TmnKt0zn3FOTfZOfe/+/v5vT6AzWyYmWVF/t0P+AywYZdzjsKbIngBcC0wxMx+uh8vsxyYYmaHmFlfvCnRi7qj/u7inLvdOTfWOTcRr743nHNXdTwnEd6HnuKcKwEKzWxapOk0Oq9lrfc7sUTll2WvD2BgFPCmma3B+4Z91Tm36xCsdOBS59xm51wYuBoo2PWJzOxhYCkwzcyKzOw68NatAHauW7EeeKzjokExRO9D97oZeCjyvXck8PNdHtf7nTii8stSa0GIiHQQ+YW5AG/x9VLgB865+8zsbLwb4TsXF/vZQb+WAlhExB+x0AUhIhKXFMAiIj5RAIuI+EQBLCLiEwWwiIhPFMAiIj5RAIvsBzN7y8y6bVdcSWwKYBERnyiAJeaZWYaZPR/ZNWWtmX3ezO40s+WR43vMzCLnvmVmvzOzFZFdLuaY2VNmlrtzHQczmxjZBeOhyDlPmFn6bl73DDNbamYfmtnjZta/p792iW0KYIkHC4HtzrnZzrkZwEvAn5xzcyLH/YBzO5zf5pzLBv4CPAPciLei2TVmNiRyzjTgz865w4E64KsdX9DMhgLfA053zh0NrAC+GbWvUOKSAljiwcfAZ8zsl2Z2onOuFjjFzJaZ2cfAqcD0Ducv6vB5Oc65Hc65ViCfT1a8KnTOvRf594PA/F1e81i8nRHei2wW8EVgQrd/ZRLXtCuyxDzn3CYzOxo4G/ipmb2Od1Wb7ZwrNLMfAmkdPqU18t9wh3/vPN75M7HrIim7HhveynyXd8OXIAlKV8AS88xsNNDknHsQ+DWfLJxeEemXveQAnna8fbIL8hXAu7s8/j5wws5NOCP90FMP4HUkgekKWOLBTODXZhYGAsB/A58F1gIleGu57q+NwI1mdj/eQux3d3zQOVduZtcAD+/clBOvT3jTAX0FkpC0HKXILsxsIvBc5AaeSNSoC0JExCe6AhYR8YmugEVEfKIAFhHxiQJYRMQnCmAREZ8ogEVEfKIAFhHxyf8H4WRFfhaHQMMAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "code",
"source": [
"for alpha in 0.5, 1.0, 5.0:\n",
" # sample & plot from bounded rejection sampling\n",
" data = pd.DataFrame.from_records([{\n",
" 'logsample' : np.log(bounded_pareto_rejection_sample(alpha=alpha, lower_bound=lower_bound, upper_bound=upper_bound)),\n",
" } for __ in range(1000)])\n",
" sns.displot(data=data, x='logsample', kind='kde')\n",
"\n",
" #expected\n",
" x = np.linspace(data['logsample'].min(), data['logsample'].max(), 100)\n",
" plt.gca().plot(x, bounded_pareto_pdf(x, alpha=alpha, lower_bound=lower_bound, upper_bound=upper_bound), 'r-', lw=5, alpha=0.6)\n",
"\n",
" plt.gca().set(yscale=\"log\")"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 1000
},
"outputId": "3c10e237-cb75-416b-a6dd-de49f682e031",
"id": "fXWx69Wxwi9f"
},
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
},
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 360x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
}
}
]
}
]
}
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