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Normal approximation of the binomial distribution
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np\n",
"import seaborn as sns\n",
"import scipy.stats\n",
"import pylab\n",
"\n",
"%matplotlib inline\n",
"%config InlineBackend.figure_format = 'retina'"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Setup"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"sns.set(color_codes = True)\n",
"sns.set_context(\"notebook\", font_scale=1, rc={\"lines.linewidth\": 1})\n",
"sns.set_style(\"white\")\n",
"sns.set_style(\"ticks\")\n",
"np.random.seed(1)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Generate data"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"n = 80000.0\n",
"p = 0.001\n",
"\n",
"norm_mean = n * p\n",
"norm_sd = np.sqrt(n * p * (1 - p))\n",
" \n",
"x_min, x_max = norm_mean - 4 * norm_sd, norm_mean + 4 * norm_sd\n",
"x_b = np.floor(np.arange(x_min, x_max, 1))\n",
"x_n = np.arange(x_min, x_max, 0.01)\n",
"\n",
"binom = scipy.stats.binom.pmf(x_b, n, p)\n",
"norm = scipy.stats.norm.pdf(x_n, loc=norm_mean, scale=norm_sd)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Plot"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"image/png": 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67fyT52ZnZ2vRokW6//77FRcXd8a5AQCwyqovd2vrriJFhAfq7msHWh2nzXI4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09XVlaW05otW7Zo1qxZatOmjeLi4pSRkaFNmzYpMTFR77//Pv27zlz1rqCgQHFxcUpJSVG3bt00\nZMgQZWVlaceOHdq3b5/WrFmj7t272+trfNszcF0VFRUZ9913nxEVFWVERUUZCQkJ9mknT540OnXq\nZIwbN864fPmyffz11183oqKijPXr19fGIsMwjEGDBhkxMTEua+ifZzp06JARFRVlPPTQQ0ZhYaF9\nfPv27UZkZKQxe/ZswzAMIz09nf6ZxJNPPml06NDB+PLLL+1jbH+e56233jIiIyONV199tdz4jBkz\njKioKCM+Pt4wDHrnqWbOnGlERUUZL7/8crnxRYsWGZGRkfTPg6SnpxsxMTFGZGSkERUVZaxdu7bc\n9Or0KD8/34iOjjaGDh1q5Ofn28c3bdpkREZGGgsXLqz5FbrBVNY/m+zsbGPChAn2Oke9yM3NNXr1\n6mUMGzbMsFqt9vGNGzcakZGRxuLFi2tsPW5ElfVu5cqVRmRkpPHKK6+UGz9w4IDRsWNH4/7777eP\nuWPb41L862zFihVKS0tT3759K0zbuHGjSkpKNGnSJHl7e9vHn3zySTVo0ECbNm1y56Li3/Ly8pSR\nkaHIyEiXdfTPM23YsEEWi0UvvfSSfH197eN33323xo4dq9atW0uS/vGPf9A/E9i6dat2796tMWPG\nqE+fPvZxtj/P869//UsWi0WjRo0qNz5mzBgZhqFDhw5JoneeqKSkRB9//LECAwMr3G42bdo0NWjQ\nQGvWrJFE/2rbmjVrdP/99yslJaXcb+KVqtOjbdu26eLFi5owYYLq169vHx89erTCwsIUHx/v8FYM\nXJ2q9E+SPvzwQ91zzz3av3+/+vXr57QHW7duVV5enh555BHVq1fPPh4bG6vWrVvrgw8+uO7rcKOq\nSu927twpLy8vTZ06tdx4r169FB0drZSUFJ0+fVqSe7Y9gv11lJycrFWrVmnSpElq27ZthemJiYmS\npOjo6HLjvr6+6tatm5KTk5WXl+eWZcV/HD16VJIqDfb0zzN9/vnnioiIsAf4K82bN0+TJk2SRP/M\noKioSEuWLFFAQICmT59ebhr98zyNGjWSJGVkZJQbz8zMlCQFBwdLkv05CfTOc2RnZ8tqtSoiIkJ1\n69YtN83X11ehoaFKSUlRfn4+/atl69atU6tWrbRhwwbdf//9Dnf8q/P7aKvt3bt3hflER0crJydH\nKSkp13s1blhV6Z9UdnCmYcOGWrVqlR577DGn8/vmm28kVey1bezcuXP66aefrs/C3+Cq0rtx48bp\n6aefVoMGDSpMs51ssj3nwh3bHsH+OiktLdWcOXMUFhZmDxK/lpaWpuDg4HJH2GxatmwpSQ4f9oWa\ndfToUVksFmVnZ2vixImKjo5WdHS0pk6dqp9//tleR/88T3Z2trKzs9WuXTsdP35cU6ZM0a233qpe\nvXpp2rRpSk9Pt9fSP8+3YcMGnTp1So899pgCAwPLTaN/nmf06NHy8fHRq6++qqSkJBUUFGj//v1a\nvHixAgMDNXr0aEnSiRMn6J2Hse1wFhUVOZyel5cnwzCUkZFB/2rZSy+9pC1btqhr165Oa6rz+5iW\nliZJCgkJqbQW164q/ZOkqVOn6qOPPtKAAQNc1qWlpclisahVq1YVptn6d+W+K65eVXo3atQoPfHE\nExXGz58/r8TERNWrV8/eF3dsewT762T16tVKTk7Wyy+/7PQhMjk5OQoICHA4rWHDhpKk3NzcGltG\nOHb06FEZhqG3335b/v7+io2NVdeuXbVz507Fxsban2pJ/zyP7fKmrKws+0OgHnjgAfXs2VM7duzQ\nb3/7W506dUoS/fN0paWlWrdunfz9/RUXF1dhOv3zPJ06ddLbb7+tS5cuKS4uTt26ddOECRPk7e2t\nd999V82bN5dE7zxRYGCgWrVqpeTkZJ08ebLctGPHjunEiROSyvpC/2pXv379HD6M+UrV6VFOTo58\nfX3L3brmrBbXrir9k6TbbrtNPj4+ldbl5OTIz8/PYdaw9Y8raK6PqvbOkUWLFik/P18xMTH2vrpj\n2yPYXwc///yzli1bpri4OHXp0sVp3eXLlx02U6r86Dlqjre3t1q2bKk1a9bof/7nfzRjxgy9+eab\neu2115Sbm6vZs2dLon+e6MrLm4YOHarNmzdr5syZWrlypf785z/r7NmzeuWVVyTRP0+3a9cunTp1\nSrGxsQ6fCkv/PE92drYWL16ss2fP6s4779TEiRPVu3dvnTp1SnPnzrXvXNI7z/TII4+ooKBATz75\npJKSkmS1WpWYmKhp06bJz89PkmQYBv0zger0qLJawzBUWFhYMwuKa0b/PN/y5csVHx+vVq1a6emn\nn7aPu6N3vJ/kOpgzZ46aNGlS4QE0v+bn56fi4mKH02w/uI4uo0LNeu655xyODx8+XBs3blRiYqJ+\n/vln+ueBbK/S8vb21p/+9KdyR1YffPBBrV27Vnv27FFBQQH983BbtmyRxWJRbGysw+n0z/NMnz5d\nBw8e1NKlS3X33Xfbx9esWaMFCxZo7ty5WrJkCb3zUA8++KB++eUXrV+/3n6VjMVi0YgRIxQdHa2N\nGzeqfv369M8EqtMjPz8/nT171mmtxWIp92AveJa6devq4sWLDqfZ+sf2WHtef/11rVixQkFBQVq5\ncqX9TLzknm2PYH+N1q9fr6SkJK1atcp+hFuSwwcsBAQEOL3EwjZ+5T8A1L6OHTsqMTFRJ0+epH8e\nyPb/d8uWLStchmixWBQZGan09HSdOnWK/nmwoqIiffnll4qMjFRoaKjDGvrnWbKysvT1118rOjq6\nXKiXpIcfflibNm3Sxx9/rPz8fHrnwWbPnq0xY8boyy+/lGEYio6OVseOHe1PeA4ODqZ/JlCdHgUE\nBKiwsFDFxcUVLv2mn54vMDBQJ06cUElJSbk3IEj0rzaVlpZq7ty52rx5s5o0aaK33367woPU3bHt\ncSn+NdqxY4csFoueeOIJRUVF2f/eeecdSdL48ePVoUMHZWRkKDQ0VOfOnXN4yVp6erq8vLzUpk0b\nd6/CDa2kpETff/+9vvvuO4fTCwoKJJUdIaV/nickJETe3t5Oz1RcvnxZUtmZCvrnuRISEnTp0qUK\nAfFK9M+z2J5dER4e7nB627ZtVVpaqtOnT9M7D9e+fXtNmDBBDz/8sDp27ChJOnz4sBo2bKimTZvS\nPxOoTo9sB09//WwFW60khYWF1dzC4pqEhoaqtLS0wttIJPpXW4qKivT73/9emzdvVkhIiN577z1F\nRERUqHPHtkewv0ajR4/W5MmTNWXKlHJ/ticoxsTEaMqUKQoICFDPnj1VWlpqf92BTVFRkQ4dOqT2\n7dtz+ZOblZSUaNy4cXr88ccdXmWRlJQkb29vdejQgf55IF9fX3Xu3FmnTp2yP+zJpqSkRMnJyWrU\nqJGaNWtG/zzYwYMHZbFY1KNHD6c19M+z2F5l5+wJvqmpqbJYLAoODqZ3Hmr69OkaOHBghf/2/fDD\nDzp58qT69+8viW3PDCrrUbt27ew96tmzpwzDsL/G8EoJCQlq2LChw1c2wzO46t+BAwcUGBjo9Mo3\n1IxnnnlGe/bsUUREhN577z2HT72X3LPtEeyv0ciRIyuE+iuD/ahRozR58mT5+/tr+PDh8vLy0htv\nvFHuqOqKFSuUn5/v9N5S1BxfX18NHjxYFy9e1KpVq8pNe+utt3Ts2DGNGDGC/nmw2NhYGYah+fPn\n28/QS2X9y8zM1MiRI2WxWOifBzty5IiksqesO0P/PEtISIg6deqkhIQE7dq1q9y0999/X0ePHtWA\nAQMUEBBA7zxUeHi4zpw5o23bttnHCgoKNH/+fFksFj3++OOS2PbMoLIejR071j42ZMgQNWjQQKtX\nr9aFCxfs45s2bVJqaqrGjBnj1mVH9dx1112qV6+eVq1aVe72i40bNyotLa1cr1Hz1q1bp507d6pN\nmzZat26dmjRp4rTWHdse99i7UXh4uCZOnKjVq1crJiZGgwYN0rFjx/TZZ5+pV69e/JjWkpkzZyop\nKUlLly7V/v37FRkZqcOHDyshIUHt27fXrFmzJNE/TzV69Gjt3r1bu3bt0siRIzVgwAD99NNP2rt3\nr8LDwzV58mRJ9M+TpaWlyc/Pz+HT8G3on+d5+eWXNWHCBD311FMaNGiQwsLClJycrH379qlZs2b2\nB5PSO8/08MMPKz4+XrNnz9a+ffsUFBSkTz75ROnp6Zo2bZo6dOggif6ZQXV6FBgYqGeffVbz5s3T\nyJEjNWzYMGVlZWn79u0KDw/XpEmTanFNUJnGjRtrxowZmj9/vn7zm99o2LBhysjI0I4dO9SuXTv7\nATnUvKKiIi1fvtz+TKf169c7rBs3bpyCg4Pdsu15v/DCCy9c81xQweeff67vvvtOMTExatmypX28\nb9++CgoK0uHDh/X555+roKBADzzwgF588UWeYllLbGeUcnNzlZSUpISEBJWWlio2NlYLFiwo91A2\n+ueZhg0bpoCAAB05ckT79u2zvzt00aJF9M8EVqxYobp16+qRRx5xWUf/PEuTJk00bNgw5ebm6sCB\nA/r6669VUFCg4cOHa/Hixbr55pvttfTO8/j6+uree+/VmTNn9PXXX+vgwYNq3bq15syZU+EsPP3z\nDMnJyfr00081YMAA+5WhNtXpUefOndW2bVsdOXJEe/fuVXZ2toYNG6aFCxeqcePG7lylG4qr/l0p\nPT1dW7duVY8ePdSvX78K07t06aKwsDAdOXJEn332mS5cuKB7771XCxYsUKNGjWpyFW5Yjnp37Ngx\nrV27VpJ0/PhxHThwwOHfiBEj7Gfya3rbsxiObiwGAAAAAACmwD32AAAAAACYGMEeAAAAAAATI9gD\nAAAAAGBiBHsAAAAAAEyMYA8AAAAAgIkR7AEAAAAAMDGCPQAAAAAAJkawBwAAAADAxAj2AAAAAACY\nGMEeAAAAAAATI9gDAAAAAGBiBHsAAAAAAEyMYA8AAAAAgIkR7AEAAAAAMDGCPQAAAAAAJkawBwAA\nAADAxAj2AAAAAACY2P8HaFlm7wXI7u0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x11daab0d0>"
]
},
"metadata": {
"image/png": {
"height": 348,
"width": 507
}
},
"output_type": "display_data"
}
],
"source": [
"pylab.scatter(x_b, binom)\n",
"pylab.plot(x_n, norm)\n",
"sns.despine()"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.12"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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