BryanSWeber/samplesfromheavytailsexperiment.ipynb

## samplesfromheavytailsexperiment.ipynb
{
  "nbformat": 4,
  "nbformat_minor": 0,
  "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": "3.7.0"
    },
    "colab": {
      "name": "SamplesFromHeavyTailsExperiment.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/gist/BryanSWeber/e39fc5838fdcd0f436c654d6de082748/samplesfromheavytailsexperiment.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e6AnX71vPKzX"
      },
      "source": [
        "# Loading Dependencies"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "QiYF3BvjiSvm"
      },
      "source": [
        "import numpy as np\n",
        "import scipy.stats\n",
        "import statistics\n",
        "import math\n",
        "# import powerlaw\n",
        "# from scipy.stats import powerlaw\n",
        "from scipy.stats import genpareto\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-CQ2SGIBPZJm"
      },
      "source": [
        "# Generating Data"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "c3hChotqiSvq"
      },
      "source": [
        "n = 10**5\n",
        "base = 1.15\n",
        "maxSteps = round(math.log(n, base))\n",
        "selectedElements = (base**np.asarray(range(round(math.log(1000, base)),maxSteps))).astype('int')\n",
        "numberSteps = len(selectedElements)\n",
        "\n",
        "averagesCumulative = np.zeros(numberSteps)\n",
        "std = np.zeros(numberSteps)\n",
        "confInterval = np.zeros(numberSteps)\n",
        "powerLevel = 1 #large enough  that there is no mean\n",
        "sampleData = genpareto.rvs(powerLevel, size=n)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "grCjQ8DZPieE"
      },
      "source": [
        "# Viewing Heavy-Tailed Data"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u50oq70-QpY9"
      },
      "source": [
        "Let us look at some basic cutoff points for the data. How much is over 10? 100? etc.?\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dxx4DuemiSvu",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "578bc896-fccc-4f6b-bab7-ee8390e27a13"
      },
      "source": [
        "sum(sampleData > 10), sum(sampleData > 100), sum(sampleData > 10000), sum(sampleData > 100000)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(9062, 1010, 8, 0)"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "t8RXmuaDiSvr",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "bb39e646-74e7-4acb-b689-6a36319e168e"
      },
      "source": [
        "plt.hist(sampleData, bins=50, density = True, log = True)\n",
        "plt.title(\"Histogram of Heavy-Tailed Data: Log Scale\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aFwWHN-BPpev"
      },
      "source": [
        "Now, we repeatedly sample from our data, seeing what happens when we add a small amount of data to our existing sample. \n",
        "\n",
        "In a non-heavy distribution (most normal cases), we'd expect some variation in the sample mean, but we would still anticipate it will be centered around some number and converge to the true mean as the sample gets larger.  This ***won't*** happen as our sample gets larger. Our distribution does not have a true mean to converge to!\n",
        "\n",
        "Furthermore, the sample standard deviation aught to also converge to the population standard deviation. Again, this will ***not*** happen. Our distribution does not have a true standard deviation to converge to either!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "JF8YD3FWiSvr"
      },
      "source": [
        "for i in range(0,numberSteps):\n",
        "    dataSelection = sampleData[0:selectedElements[i]]\n",
        "    if selectedElements[i] >= 1:\n",
        "        averagesCumulative[i] = statistics.mean(dataSelection)\n",
        "    if selectedElements[i] >= 2:\n",
        "        std[i] = statistics.stdev(dataSelection)\n",
        "        confInterval[i] = statistics.stdev(dataSelection)/math.sqrt(selectedElements[i]) * 1.96"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": false,
        "id": "PCxOtf4PiSvs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "aa48abb8-cde6-41b0-c60e-3375a456ffe5"
      },
      "source": [
        "#plt.plot(sampleData[0:n], label = \"Raw Data\")\n",
        "#plt.plot(averagesCumulative[0:(n-1)], label = \"Cumulative Average\")\n",
        "plt.errorbar(selectedElements, averagesCumulative, yerr = confInterval, label  = \"95% CI of Sample Average\")\n",
        "plt.legend()\n",
        "plt.title(\"Regression to the Tail: Increasing Sample Means\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "scrolled": true,
        "id": "pdXjiKkKiSvu",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "edc23840-5195-432f-b619-dc0b6b6239cc"
      },
      "source": [
        "plt.plot(selectedElements,std, label = \"Cumulative Std\")\n",
        "plt.title(\"Regression to the Tail: Sample Standard Errors\")\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ShHOlxJ4RIgb"
      },
      "source": [
        "**Amazing**.  Both the mean and the standard deviation of our samples simply march upward in spurts.  They don't seem to settle anywhere.  With investigation, we will see the \"spurts\" align with new, very large observations. This is a big problem for an analyst who wants to examine with a sample size of a hundred... or a thousand... or any size. Later, we will discuss some ways to discuss this data meaningfully."
      ]
    }
  ]
}