Assignment.ipynb

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    "colab": {
      "name": "Assignment.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "authorship_tag": "ABX9TyO9IFB1DscvFYiP6TBaD/Gh",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/Ipsit1234/SHALA/blob/master/Assignment.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NVMUAJt8gzbA",
        "colab_type": "text"
      },
      "source": [
        "# MLE and Hypothesis Testing"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d1-kEc8hXx3N",
        "colab_type": "text"
      },
      "source": [
        "### Read the given csv file [```q4.csv```](https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4.csv) of samples. Assume that it is drawn from a exponential distribution. What is the difference of log likelihoods for $\\lambda = 1$ and $\\lambda = 2$ ? Which of the two is more strongly supported?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DHfUkvD3KcNN",
        "colab_type": "code",
        "outputId": "84aa3287-97b2-4dec-ba7b-8190925ed0d7",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from scipy import stats\n",
        "from matplotlib import pyplot as plt\n",
        "import seaborn as sns"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UAphR126LEwa",
        "colab_type": "code",
        "outputId": "0da3c8fe-cb2d-4481-9f7f-84b22372b7ad",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 195
        }
      },
      "source": [
        "url = 'https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4.csv'\n",
        "data = pd.read_csv(url,header=None)\n",
        "data.head()"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
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              "\n",
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              "<table border=\"1\" class=\"dataframe\">\n",
              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>0</th>\n",
              "      <th>1</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>0</td>\n",
              "      <td>0.019404</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.043634</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.023797</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>0.444340</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.578160</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   0         1\n",
              "0  0  0.019404\n",
              "1  1  0.043634\n",
              "2  2  0.023797\n",
              "3  3  0.444340\n",
              "4  4  0.578160"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nDpo9jpidQHk",
        "colab_type": "text"
      },
      "source": [
        "# PDF of exponential distribution is $\\lambda e^{-\\lambda x}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hio8uXrtLjl7",
        "colab_type": "code",
        "outputId": "0da578f0-e3ff-4f9c-a55e-08c11d9994d1",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "def pdf_exp(lamb,x):\n",
        "\treturn lamb * np.exp(-1*lamb*x)\n",
        "\n",
        "likelihood1 = 1\n",
        "likelihood2 = 1\n",
        "for aa in data[1].values:\n",
        "  likelihood1 = likelihood1 * pdf_exp(x = aa,lamb=1)\n",
        "  likelihood2 = likelihood2 * pdf_exp(x = aa,lamb=2)\n",
        "log_likelihood1 = np.log(likelihood1)\n",
        "log_likelihood2 = np.log(likelihood2)\n",
        "print(log_likelihood1 - log_likelihood2)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "-20.366416970604874\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q214ixOGeR35",
        "colab_type": "text"
      },
      "source": [
        "### Read the csv files [```q4_1.csv```](https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_1.csv) and [```q4_2.csv```](https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_2.csv) to get samples from two unknown distributions. Choose a significance level and implement the the most general two-sample t-test"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bAsMqWiGdb52",
        "colab_type": "code",
        "outputId": "448ac69e-e6d1-490b-df76-f6a69929470a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 218
        }
      },
      "source": [
        "sample1 = pd.read_csv('https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_1.csv',header=None)\n",
        "sample2 = pd.read_csv('https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4_2.csv',header=None)\n",
        "print(sample1.head())\n",
        "print(sample2.head())"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "   0         1\n",
            "0  0 -0.179278\n",
            "1  1  0.236714\n",
            "2  2  0.255502\n",
            "3  3 -0.029321\n",
            "4  4  0.004818\n",
            "   0         1\n",
            "0  0  0.680541\n",
            "1  1  0.436810\n",
            "2  2  0.604089\n",
            "3  3  0.518702\n",
            "4  4  0.479711\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_3TBrHZifG2u",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "significance = 0.05\n",
        "mu1 = np.mean(sample1[1].values)\n",
        "mu2 = np.mean(sample2[1].values)\n",
        "s1 = np.var(sample1[1].values)\n",
        "s2 = np.var(sample2[1].values)\n",
        "n1 = sample1[1].shape[0]\n",
        "n2 = sample1[1].shape[0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p4Hx9UL3flF8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "T = (mu1 - mu2) / np.sqrt((s1/n1) + (s2 / n2))\n",
        "df = np.square((s1/n1) + (s2 / n2)) / (((s1/n1)**2)/(n1-1) + ((s2/n2)**2)/(n2-1))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ST8J42mAfn0R",
        "colab_type": "code",
        "outputId": "d4729d20-e194-4d93-b780-3acb4c721503",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "critical_value = stats.t.pdf((1-significance)/2,df)\n",
        "print('T : {}, Critical Value : {}'.format(np.abs(T),critical_value))\n",
        "if np.abs(T) > critical_value:\n",
        "  print('Null hypothesis is rejected')\n",
        "else:\n",
        "  print('Null hypothesis is not rejected')"
      ],
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "T : 18.292145241166835, Critical Value : 0.35547474461325235\n",
            "Null hypothesis is rejected\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "omfVDZqxfyAM",
        "colab_type": "code",
        "outputId": "46dece49-758d-4830-9865-976145d664f3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        }
      },
      "source": [
        "sns.distplot(sample1[1].values)\n",
        "\n",
        "sns.distplot(sample2[1].values)\n",
        "plt.legend(['first sample','second sample'])\n",
        "plt.show()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z-5ammelgOnA",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": 0,
      "outputs": []
    }
  ]
}