Distributions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Examples of Data Distributions"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Uniform Distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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": [
    "%matplotlib inline\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "values = np.random.uniform(-10.0, 10.0, 100000)\n",
    "plt.hist(values, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Normal / Gaussian"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualize the probability density function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-3.    -2.999 -2.998 ...  2.997  2.998  2.999]\n",
      "[0.00443185 0.00444516 0.00445851 ... 0.00447189 0.00445851 0.00444516]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe8aa68d7f0>]"
      ]
     },
     "execution_count": 3,
     "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",
    "\n",
    "x = np.arange(-3, 3, 0.001)\n",
    "print(x)\n",
    "print(norm.pdf(x))\n",
    "plt.plot(x,norm.pdf(x))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate some random numbers with a normal distribution. \"mu\" is the desired mean, \"sigma\" is the standard deviation:"
   ]
  },
  {
   "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": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "mu = 0\n",
    "sigma = 2.0\n",
    "values = np.random.normal(mu, sigma, 10000)\n",
    "plt.hist(values, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exponential PDF / \"Power Law\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe8a9d265f8>]"
      ]
     },
     "execution_count": 18,
     "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 expon\n",
    "import matplotlib.pyplot as plt\n",
    "import math\n",
    "x = np.arange(0, 10, 0.001)\n",
    "\n",
    "x=[0,1,2]\n",
    "out=list(map(lambda x:math.sin(x),x))\n",
    "\n",
    "plt.plot(x,out)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Binomial Probability Mass Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.000e+00 1.000e-03 2.000e-03 ... 9.997e+00 9.998e+00 9.999e+00]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe8a9bf8940>]"
      ]
     },
     "execution_count": 20,
     "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 binom\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "n, p = 10, 0.5\n",
    "x = np.arange(0, 10, 0.001)\n",
    "print(x)\n",
    "\n",
    "plt.plot(x, binom.pmf(x, n, p))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson Probability Mass Function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example: My website gets on average 500 visits per day. What's the odds of getting 550?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7fe8a92e8eb8>]"
      ]
     },
     "execution_count": 31,
     "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",
    "\n",
    "averagesale = 500\n",
    "x = np.random.normal(500,1000,11)\n",
    "z\n",
    "print(x)\n",
    "plt.plot(x, poisson.pmf(x, averagesale))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pop Quiz!"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What's the equivalent of a probability distribution function when using discrete instead of continuous data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   7.,   59.,  355., 1207., 2469., 2851., 1972.,  858.,  201.,\n",
       "          21.]),\n",
       " array([-3476.74108686, -2731.66379086, -1986.58649487, -1241.50919887,\n",
       "         -496.43190287,   248.64539313,   993.72268913,  1738.79998512,\n",
       "         2483.87728112,  3228.95457712,  3974.03187312]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 27,
     "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": [
    "plt.hist(x)"
   ]
  },
  {
   "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": "3.6.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}