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Shapes and definition of some statistical PDFs, handy to do some modelling. You can see the rendered version on nbviewer here: http://nbviewer.ipython.org/urls/gist.github.com/mattions/6113437/raw/c5468ea930d6960225d83e112d7f3d00d9c13398/Exploring+different+distribution.ipynb
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"cells": [
{
"cell_type": "code",
"collapsed": false,
"input": [
"%matplotlib inline\n",
"import numpy as np\n",
"import matplotlib\n",
"import matplotlib.pyplot as plt\n",
"import scipy.stats\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"%autosave 30"
],
"language": "python",
"metadata": {},
"outputs": [
{
"javascript": [
"IPython.notebook.set_autosave_interval(30000)"
],
"metadata": {},
"output_type": "display_data"
},
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Autosaving every 30 seconds\n"
]
}
],
"prompt_number": 2
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Statistical distribution\n",
"========================\n",
"\n",
"Let's have a look how different statistical distributions look like, to have a better\n",
"idea what to use as prior on our inference bayesian exploration.\n",
"\n",
"All the distributions available in scipy can be found on the docs here: http://docs.scipy.org/doc/scipy/reference/stats.html#module-scipy.stats\n",
"\n",
"Let's start with Discrete distributions\n",
"\n",
"Discrete Distributions\n",
"----------------------\n",
"\n",
"\n",
"* bernoulli:\tA Bernoulli discrete random variable.\n",
"* binom:\tA binomial discrete random variable.\n",
"* poisson:\tA Poisson discrete random variable.\n",
"* ...\n",
"\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"from scipy.stats import bernoulli, poisson, binom"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 3
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bernoulli distribution\n",
"-----------------------\n",
"\n",
"Given a certain probability $p$, the Bernoulli distribution takes value $k=1$, meanwhile \n",
"it takes $k=0$ in all the other cases $1-p$.\n",
"\n",
"In other words:\n",
"\n",
"$$\n",
"f(k;p) = \\begin{cases}\n",
" p & \\text{if } k=1 \\\\\\\\ \n",
" 1-p & \\text{if } k=0\n",
"\\end{cases}\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"bernoulli.rvs(0.6, size=100)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 4,
"text": [
"array([1, 1, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 1, 0,\n",
" 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1, 0, 1, 0, 0,\n",
" 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1,\n",
" 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 1,\n",
" 1, 1, 1, 1, 1, 1, 1, 0])"
]
}
],
"prompt_number": 4
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"a = np.arange(2)\n",
"\n",
"colors = matplotlib.rcParams['axes.color_cycle']\n",
"plt.figure(figsize=(12,8))\n",
"for i, p in enumerate([0.1, 0.2, 0.6, 0.7]):\n",
" ax = plt.subplot(1, 4, i+1)\n",
" plt.bar(a, bernoulli.pmf(a, p), label=p, color=colors[i], alpha=0.5)\n",
" ax.xaxis.set_ticks(a)\n",
"\n",
" plt.legend(loc=0)\n",
" if i == 0:\n",
" plt.ylabel(\"PDF at $k$\")\n",
" \n",
"\n",
"plt.suptitle(\"Bernoulli probability\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 18,
"text": [
"<matplotlib.text.Text at 0x6df5c10>"
]
},
{
"metadata": {},
"output_type": "display_data",
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4cULZ2dlh19bX13f7OtGOPzznX4xVVVXdrtr15/hcg7n/cDq2Q3aH/ri2ttbx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\nQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x67edbd0>"
]
}
],
"prompt_number": 18
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Poisson Distribution\n",
"--------------------\n",
"\n",
"Another discrete distribution, the *Poisson Distribution* is defined for all the integer positive number as\n",
"\n",
"$$P(Z=k)=\\frac{\u03bb^ke^{\u2212\u03bb}}{k!}, k=0,1,2, \\ldots$$\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = np.arange(20)\n",
"colors = matplotlib.rcParams['axes.color_cycle'] \n",
"plt.figure(figsize=(12,8))\n",
"for i, lambda_ in enumerate([1, 4, 6, 12]):\n",
" plt.bar(k, poisson.pmf(k, lambda_), label=lambda_, color=colors[i], alpha=0.4, edgecolor=colors[i], lw=3)\n",
" plt.legend()\n",
"plt.title(\"Poisson distribution\")\n",
"plt.xlabel(\"$k$\")\n",
"plt.ylabel(\"PDF at k\")\n",
" \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 6,
"text": [
"<matplotlib.text.Text at 0x4642e10>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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Fb8IrjAVuSZoxY0bqftoHW7RoUbf15MmT9dBDDx3VOQAAAIChgE+aBFzAHCJs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\nAvx8pKpqAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x42cba10>"
]
}
],
"prompt_number": 6
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"k = np.arange(15)\n",
"plt.figure(figsize=(12,8))\n",
"for i, lambda_ in enumerate([1, 2, 4, 6]):\n",
" plt.plot(k, poisson.pmf(k, lambda_), '-o', label=lambda_, color=colors[i])\n",
" plt.fill_between(k, poisson.pmf(k, lambda_), color=colors[i], alpha=0.5)\n",
" plt.legend()\n",
"plt.title(\"Poisson distribution\")\n",
"plt.ylabel(\"PDF at $k$\")\n",
"plt.xlabel(\"$k$\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 16,
"text": [
"<matplotlib.text.Text at 0x5d5ea90>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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iIqJecOY7Bqw9ZMWlw9Pws3EDRZdCREREFHc48x1nspJ02FrdKroMIiIiIuoF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\nzn0VRcHixYtRWFjY2Xj3doxIsVdaoUk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+6+h13p9IE7lLdYn1V49Ye3WJ9deO6O4iIsB7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TAAAg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\nhBBCZMj/B5O8oxYJaLgEAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x6032110>"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Binomial distribution\n",
"---------------------\n",
"\n",
"Last but not least, the binomial distribution which is defined as:\n",
"\n",
"$$f(k;n,p) = Pr(X = k) = {n \\choose k} p^k (1-p)^{(n-k)}$$\n",
"\n",
"where \n",
"\n",
"$${n \\choose k} = \\frac{n!}{k!(n-k)!}$$\n",
"\n",
"with $k={1, 2, 3, \\ldots}$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure(figsize=(12,6))\n",
"k = np.arange(0, 22)\n",
"for p, color in zip([0.1, 0.3, 0.6, 0.8], colors):\n",
" rv = binom(20, p)\n",
" plt.plot(k, rv.pmf(k), lw=2, color=color, label=p)\n",
" plt.fill_between(k, rv.pmf(k), color=color, alpha=0.5)\n",
"plt.legend()\n",
"plt.title(\"Binomial distribution\")\n",
"plt.tight_layout()\n",
"plt.ylabel(\"PDF at $k$\")\n",
"plt.xlabel(\"$k$\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 15,
"text": [
"<matplotlib.text.Text at 0x5ad0710>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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N6JwWCQBDhw5FZGQkamtrvRd0P5Wc6WwkEhGA69Nc9GEKGNUKWO1OHK9pkTsc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\ngHFXpSFjeAxUYYGTWzHx4RgyKhYAsOn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ug62+or2P1GUsnaoqNK3L1wnu2NJN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/Xz8XgclGLoD9rwTbA3HcJ8uzAjcSn8/eX5zJ73nx7kiiVrAXjo19/i5ZdfHn99y5YtZyVV8lye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\nbj+tXKxangAAAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x5d4cdd0>"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Continous Probability Distribution\n",
"----------------------------------\n",
"\n",
"They are defined for any value of a positive $x$. A lot of distribution are defined on `scipy.stats`, so I will explore only som:\n",
"\n",
"* alpha\tAn alpha continuous random variable.\n",
"* beta\tA beta continuous random variable.\n",
"* gamma\tA gamma continuous random variable.\n",
"* expon\tAn exponential continuous random variable.\n",
"* ..."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Alpha\n",
"-----\n",
"\n",
"The Alpha distribution is defined as \n",
"\n",
"$$\n",
"alpha.pdf(x,a) = \\frac{1}{x^2 \\Phi(a) \\sqrt{2*pi}} * exp(-\\frac{1}{2} (\\frac{a-1}{x})^2), \\,\\, with \\, x > 0, a > 0\n",
"$$\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.linspace(0.1, 2, 100)\n",
"alpha = scipy.stats.alpha\n",
"alphas = [0.5, 1, 2, 4]\n",
"plt.figure(figsize=(12,6))\n",
"for a,c in zip(alphas,colors):\n",
" \n",
" label=r\"$\\alpha$ = {0:.1f}\".format(a)\n",
" plt.plot(x, alpha.pdf(x, a), lw=2, \n",
" color=c, label=label)\n",
" plt.fill_between(x, alpha.pdf(x, a), color=c, alpha = .33)\n",
" \n",
"\n",
"plt.ylabel(\"PDF at $x$\")\n",
"plt.xlabel(\"$x$\")\n",
"plt.title(\"Alpha distribution\")\n",
"\n",
"plt.legend()\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 9,
"text": [
"<matplotlib.legend.Legend at 0x4d61210>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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LBVqtFtddd905z1uyZAnKysq6PHoroAFg4cKFqKur8zymTp2KVatWdSqgKysr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\ngg==\n",
"text": [
"<matplotlib.figure.Figure at 0x4e694d0>"
]
}
],
"prompt_number": 9
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Beta distribution\n",
"-----------------\n",
"\n",
"The Beta distribution is defined for a variabile rangin between 0 and 1. \n",
"\n",
"The pdf is defined as:\n",
"\n",
"$$\n",
"beta.pdf(x, \\alpha, \\beta) = \\frac{1}{B(\\alpha, \\beta)}x^{\\alpha-1}(1 - x)^{\\beta-1}, \\; with \\; 0\u2264x\u22641, \\alpha>0, \\beta>0\n",
"$$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"beta = scipy.stats.beta\n",
"x = np.linspace(0,1, num=200)\n",
"\n",
"\n",
"fig = plt.figure(figsize=(12,6))\n",
"for a, b, c in zip([0.5, 0.5, 1, 2, 3], [0.5, 1, 3, 2, 5], colors):\n",
" plt.plot(x, beta.pdf(x, a, b), lw=2, \n",
" c=c, label = r\"$\\alpha = {0:.1f}, \\beta={1:.1f}$\".format(a, b))\n",
" plt.fill_between(x, beta.pdf(x, a, b), color=c, alpha = .1)\n",
" \n",
" \n",
"plt.legend(loc=0)\n",
"plt.ylabel(\"PDF at $x$\")\n",
"plt.xlabel(\"$x$\")\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 14,
"text": [
"<matplotlib.text.Text at 0x5ad0f50>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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YUmZmJnbu3Amz2YyamhqYzWa0trbCYDBg0qRJUCq9q5EyMzNx/PhxHDx4EB98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zGJPTm9JmhHMz3aznQcZzpOcjoO1/qyvgaAXhzMhGxzRcheGbj1YAC7rQW7rcW9KJVCHxpzQ/XA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\n",
"text": [
"<matplotlib.figure.Figure at 0x5acc410>"
]
}
],
"prompt_number": 14
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Gamma distribution\n",
"------------------\n",
"\n",
"The gamma distribution uses the Gamma function (http://en.wikipedia.org/wiki/Gamma_function) and it has two shape parameters.\n",
"\n",
"$$\n",
"gamma.pdf(x, \\alpha, scale) = \\lambda^\\alpha * x^{(\\alpha-1)} * \\frac{exp(-\\lambda * x)}{\\gamma(\\alpha)}, \\, with \\, x >= 0, \\alpha> 0, \\lambda > 0\n",
"$$\n",
"\n",
"The scale parameter is equal = $1.0/\\lambda$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"gamma = scipy.stats.gamma\n",
"plt.figure(figsize=(12, 6))\n",
"x = np.linspace(0, 10, num=200)\n",
"\n",
"for a, c in zip([0.5, 1, 2, 3, 10], colors):\n",
" plt.plot(x, gamma.pdf(x, a), lw=2, \n",
" c=c, label = r\"$\\alpha = {0:.1f}$\".format(a))\n",
" plt.fill_between(x, gamma.pdf(x, a), color=c, alpha = .1)\n",
" \n",
"plt.legend(loc=0)\n",
"plt.title(\"Gamma distribution with scale=1\")\n",
"plt.ylabel(\"PDF at $x$\")\n",
"plt.xlabel(\"$x$\")"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "pyout",
"prompt_number": 13,
"text": [
"<matplotlib.text.Text at 0x5ae4810>"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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uqKhASEgI9uzZg6+//hohISEoLy9369w63ghEOGpa77GnYXZiY37iYnZiY37q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\n",
"text": [
"<matplotlib.figure.Figure at 0x5663190>"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Exponential\n",
"-----------\n",
"\n",
"The Exponantial probability function is\n",
"\n",
"$$ f_X(x|\u03bb) = \u03bb e^{\u2212\u03bbx} , \\, x\u22650$$\n",
"\n",
"Therefore, the random variable X has an exponential distribution with parameter \u03bb, we say X is exponential and write\n",
"\n",
"$$ X\u223cExp(\u03bb) $$\n",
"\n",
"Given a specific \u03bb, the expected value of an exponential random variable is equal to the inverse of \u03bb, that is:\n",
"\n",
"$$ E[X|\u03bb]= \\frac{1}{\u03bb} $$"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"x = np.linspace(0,4, 100)\n",
"expo = scipy.stats.expon\n",
"lambda_ = [0.5, 1, 2, 4]\n",
"plt.figure(figsize=(12,4))\n",
"for l,c in zip(lambda_,colors):\n",
" plt.plot(x, expo.pdf(x, scale=1./l), lw=2, \n",
" color=c, label = \"$\\lambda = %.1f$\"%l)\n",
" plt.fill_between(x, expo.pdf(x, scale=1./l), color=c, alpha = .33)\n",
" \n",
"plt.legend()\n",
"plt.ylabel(\"PDF at $x$\")\n",
"plt.xlabel(\"$x$\")\n",
"plt.title(\"Probability density function of an Exponential random variable;\\\n",
" differing $\\lambda$\");"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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A1Grb/ony+OOP46233sLWrVtx7NixBs8//MILL+Dtt9/G0qVLcerUKRw+fBiLFy82OwOD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\nguU/vPXK29gy0f3888/z9NNPA3D48GEOHTrUkbKCsJkoFA4eDh7dpre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"text": [
"<matplotlib.figure.Figure at 0x5656b50>"
]
}
],
"prompt_number": 12
},
{
"cell_type": "code",
"collapsed": false,
"input": [],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
}
],
"metadata": {}
}
]
}
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