{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Principais modelos probabilísticos\n",
    "\n",
    "#### SME0221 Introdução à Inferência Estatística\n",
    "\n",
    "\n",
    "\n",
    "por **Cibele Russo** \n",
    "\n",
    "**ICMC/USP - São Carlos SP**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principais modelos discretos\n",
    "\n",
    "https://docs.scipy.org/doc/scipy/tutorial/stats/discrete.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bernoulli"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "from scipy.stats import bernoulli\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#Calculate the first four moments:\n",
    "\n",
    "p = 0.3\n",
    "mean, var, skew, kurt = bernoulli.stats(p, moments='mvsk')\n",
    "\n",
    "#Display the probability mass function (pmf):\n",
    "\n",
    "x = np.arange(bernoulli.ppf(0.01, p),\n",
    "              bernoulli.ppf(0.99, p))\n",
    "ax.plot(x, bernoulli.pmf(x, p), 'bo', ms=8, label='bernoulli pmf')\n",
    "ax.vlines(x, 0, bernoulli.pmf(x, p), colors='b', lw=5, alpha=0.5)\n",
    "\n",
    "#Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.\n",
    "\n",
    "#Freeze the distribution and display the frozen pmf:\n",
    "\n",
    "rv = bernoulli(p)\n",
    "ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,\n",
    "        label='frozen pmf')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Binomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import binom\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#Calculate the first four moments:\n",
    "\n",
    "n, p = 5, 0.4\n",
    "mean, var, skew, kurt = binom.stats(n, p, moments='mvsk')\n",
    "\n",
    "#Display the probability mass function (pmf):\n",
    "\n",
    "x = np.arange(binom.ppf(0.01, n, p),\n",
    "              binom.ppf(0.99, n, p))\n",
    "ax.plot(x, binom.pmf(x, n, p), 'bo', ms=8, label='binom pmf')\n",
    "ax.vlines(x, 0, binom.pmf(x, n, p), colors='b', lw=5, alpha=0.5)\n",
    "\n",
    "#Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.\n",
    "\n",
    "#Freeze the distribution and display the frozen pmf:\n",
    "\n",
    "rv = binom(n, p)\n",
    "ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,\n",
    "        label='frozen pmf')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Geométrica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import geom\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#Calculate the first four moments:\n",
    "\n",
    "p = 0.5\n",
    "mean, var, skew, kurt = geom.stats(p, moments='mvsk')\n",
    "\n",
    "#Display the probability mass function (pmf):\n",
    "\n",
    "x = np.arange(geom.ppf(0.01, p),\n",
    "              geom.ppf(0.99, p))\n",
    "ax.plot(x, geom.pmf(x, p), 'bo', ms=8, label='geom pmf')\n",
    "ax.vlines(x, 0, geom.pmf(x, p), colors='b', lw=5, alpha=0.5)\n",
    "#Alternatively, the distribution object can be called (as a function) to fix the shape and location. This returns a “frozen” RV object holding the given parameters fixed.\n",
    "\n",
    "#Freeze the distribution and display the frozen pmf:\n",
    "\n",
    "rv = geom(p)\n",
    "ax.vlines(x, 0, rv.pmf(x), colors='k', linestyles='-', lw=1,\n",
    "        label='frozen pmf')\n",
    "ax.legend(loc='best', frameon=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.LineCollection at 0x7fcec8333dd8>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import poisson\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#Calculate the first four moments:\n",
    "\n",
    "mu = 2\n",
    "mean, var, skew, kurt = poisson.stats(mu, moments='mvsk')\n",
    "\n",
    "#Display the probability mass function (pmf):\n",
    "\n",
    "x = np.arange(poisson.ppf(0.01, mu),\n",
    "              poisson.ppf(0.99, mu))\n",
    "ax.plot(x, poisson.pmf(x, mu), 'bo', ms=8, label='poisson pmf')\n",
    "ax.vlines(x, 0, poisson.pmf(x, mu), colors='b', lw=5, alpha=0.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hipergeométrica"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import hypergeom\n",
    "import matplotlib.pyplot as plt\n",
    "#Suppose we have a collection of 20 animals, of which 7 are dogs. Then if we want to know the probability of finding a given number of dogs if we choose at random 12 of the 20 animals, we can initialize a frozen distribution and plot the probability mass function:\n",
    "\n",
    "[M, n, N] = [20, 7, 12]\n",
    "rv = hypergeom(M, n, N)\n",
    "x = np.arange(0, n+1)\n",
    "pmf_dogs = rv.pmf(x)\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111)\n",
    "ax.plot(x, pmf_dogs, 'bo')\n",
    "ax.vlines(x, 0, pmf_dogs, lw=2)\n",
    "ax.set_xlabel('# of dogs in our group of chosen animals')\n",
    "ax.set_ylabel('hypergeom PMF')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Principais modelos contínuos\n",
    "\n",
    "https://docs.scipy.org/doc/scipy/tutorial/stats/continuous.html"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Uniforme"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fce93850a90>]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import uniform\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "#Calculate the first four moments:\n",
    "\n",
    "mean, var, skew, kurt = uniform.stats(moments='mvsk')\n",
    "#Display the probability density function (pdf):\n",
    "\n",
    "x = np.linspace(uniform.ppf(0.01),\n",
    "                uniform.ppf(0.99), 100)\n",
    "ax.plot(x, uniform.pdf(x),\n",
    "       'r-', lw=5, alpha=0.6, label='uniform pdf')\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Normal"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fce9393a940>]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "#Calculate the first four moments:\n",
    "\n",
    "mean, var, skew, kurt = norm.stats(moments='mvsk')\n",
    "#Display the probability density function (pdf):\n",
    "\n",
    "x = np.linspace(norm.ppf(0.01),\n",
    "                norm.ppf(0.99), 100)\n",
    "ax.plot(x, norm.pdf(x),\n",
    "       'r-', lw=5, alpha=0.6, label='norm pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### t-Student"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fce9383bb00>]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import t\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#Calculate the first four moments:\n",
    "\n",
    "df = 2.74\n",
    "mean, var, skew, kurt = t.stats(df, moments='mvsk')\n",
    "\n",
    "#Display the probability density function (pdf):\n",
    "\n",
    "x = np.linspace(t.ppf(0.01, df),\n",
    "                t.ppf(0.99, df), 100)\n",
    "ax.plot(x, t.pdf(x, df),\n",
    "       'r-', lw=5, alpha=0.6, label='t pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Qui-quadrado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fce936f6e48>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import chi2\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#Calculate the first four moments:\n",
    "\n",
    "df = 55\n",
    "mean, var, skew, kurt = chi2.stats(df, moments='mvsk')\n",
    "\n",
    "#Display the probability density function (pdf):\n",
    "\n",
    "x = np.linspace(chi2.ppf(0.01, df),\n",
    "                chi2.ppf(0.99, df), 100)\n",
    "ax.plot(x, chi2.pdf(x, df),\n",
    "       'r-', lw=5, alpha=0.6, label='chi2 pdf')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fce936dc5f8>]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from scipy.stats import f\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(1, 1)\n",
    "\n",
    "#Calculate the first four moments:\n",
    "\n",
    "dfn, dfd = 29, 18\n",
    "mean, var, skew, kurt = f.stats(dfn, dfd, moments='mvsk')\n",
    "\n",
    "#Display the probability density function (pdf):\n",
    "\n",
    "x = np.linspace(f.ppf(0.01, dfn, dfd),\n",
    "                f.ppf(0.99, dfn, dfd), 100)\n",
    "ax.plot(x, f.pdf(x, dfn, dfd),\n",
    "       'r-', lw=5, alpha=0.6, label='f pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}