Assignment_4_DS_BasicStatistics.ipynb

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  "metadata": {
    "colab": {
      "name": "Assignment_4_DS.ipynb",
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      "include_colab_link": true
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    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/sp1999/SHALA2020/blob/master/Assignment_4_DS.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": "92736c14-e6c3-486c-c60e-4fd8a8527bd0",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 71
        }
      },
      "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": 2,
      "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",
        "colab": {}
      },
      "source": [
        "url = 'https://raw.githubusercontent.com/Ipsit1234/SHALA/master/q4.csv'\n",
        "data = pd.read_csv(url,header=None)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DEidTFh9p51d",
        "colab_type": "code",
        "outputId": "31e984e0-706f-4485-c32a-913fd7888a87",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "data.head(5)"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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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",
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            ],
            "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": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nDpo9jpidQHk",
        "colab_type": "text"
      },
      "source": [
        "# PDF of exponential distribution is $\\lambda e^{-\\lambda x}$\n",
        "Define a function to find pdf. You can use any module to get pre-defined functions also. And then find the likelihood and log-likelihood"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hio8uXrtLjl7",
        "colab_type": "code",
        "outputId": "95ca2fec-f3fc-4838-fd41-8cdb70478868",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "def pdf_exp(lamb,x):\n",
        "\treturn lamb * np.exp(-1*lamb*x)\n",
        "likelihood1 = 1\n",
        "likelihood2 = 1\n",
        "for a in data[1].values:\n",
        "\tlikelihood1 = likelihood1 * pdf_exp(x = a,lamb=2)\n",
        "\tlikelihood2 = likelihood2 * pdf_exp(x = a,lamb=1)\n",
        "log_likelihood1 = np.log(likelihood1)\n",
        "log_likelihood2 = np.log(likelihood2)\n",
        "print('log likelihood for lambda = 2 - log likelihood for lambda = 1 : ',log_likelihood1 - log_likelihood2)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "log likelihood for lambda = 2 - log likelihood for lambda = 1 :  20.366416970604874\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LrFqlPI_sAdq",
        "colab_type": "code",
        "outputId": "74f1d6de-016c-4d31-9e6c-a2f6242cac41",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        }
      },
      "source": [
        "sns.distplot(data[1].values)\n",
        "plt.show()"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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ufm64u4HnAYwxOwAXkOCNAoNd/+AgZ5q6gmL9lvGEOux8+Yo57Ctr5q1TepWulLd5Euh7gLkikiMiIQzd9NxyTpsy4EoAEVnAUKBrn4oHqpq76R80ZARx//lwNy3LIC0mjIf/ekKv0pXysnED3RjTD9wLvAIcY2g0yxEReVBErnc3+zrweRF5F9gE3Gn0X6tHgnVC0WhCHDb++epc3q1o4c8Hq6wuR6mg4vCkkTFmK0M3O4c/98Cwx0eB1d4tbXoobewkJsxJVFhwTSgay8eXpLFxWzE/eOU4H1qYTKjDbnVJSgWF4L4LFwDK3ROKphO7TfjX6xZQ3tjFsztKrS5HqaChgW6hyuYuWrr6gnr8+WjW5CZy2dwEfvpaIS2duveoUt6ggW6hfWVNQHBPKBrL/dcuoLW7j0feKLS6FKWCgga6hfaWNuG0CzOjg3dC0VjyUqO4cUk6T71T8t5sWaXUxGmgW2hfWTNpMeHYbcG3IJen/s81uYjA//vrCatLUSrgeTTKRXlfd98AR860sHpO4M2/em5XmVdfb+WseP5woJK0mHC+sX6eV19bqelEr9AtcrCihf5BM237z4dbm5tIeIidlw5V6mQjpSZBA90iZ2+ITpcZomNxOe1cnZdMSUOnTjZSahI00C2yt7SJ7PhwIkK11wvg4uw4Zka7+O+tx+jqHbC6HKUCkga6BYwx7C9rYmlWrNWl+A2bCB+5MJXKlm4efbPI6nKUCkga6BYoa+ykvr2XpZka6MPlJMzgoxel8os3i3QYo1IToIFugbP958v0Cv0D7r92PjYR/mvrMatLUSrgaKBbYG9pExGhDnKTI60uxe+kxoTxpXWzeflwNduLdM10pc6HBroF9pY2szgjZlpPKBrL59fMIj02jO9tOUr/wKDV5SgVMDTQp1h7Tz8nqltZmhljdSl+y+W0828fzuNETRvP7tTVGJXylAb6FHu3vJlBg45wGcc1C5NZk5vIw389SW1rt9XlKBUQNNCn2N7SJkRgSYYG+lhEhAevX0jPwCD/qTdIlfKIBvoU21PSSG5SJNHh02eHoonKTpjBPWtn88cDlWwv1BukSo3Ho0AXkfUickJECkXkvlHafEpEjorIERF5zrtlBoeBQcP+smbys/Xq3FP3rJtNVnw4//bHw/T26w1SpcYybqCLiB14BLgWyANuEZG8c9rMBe4HVhtjFgJf9UGtAe94dSvtPf0a6OfB5bTz3esXUlzXwRPbiq0uRym/5skV+nKg0BhTbIzpBTYDN5zT5vPAI8aYJgBjTK13ywwOe0uHJhTlZ8VZXElguXxeEtcuSuEnfz+lM0iVGoMngZ4GlA/7usL93HC5QK6IvCMiO0Vk/UgvJCIbRKRARArq6uomVnEAKyhpIjkqlPTY6blD0WR8+yN52G3C9/50xOpSlPJb3rop6gDmAuuAW4AnROQDA62NMY8bY/KNMfmJiYleeuvAUVDSSH52HCI6oeh8pcaE8dWr5vK3Y7W8erTG6nKU8kueBPoZIGPY1+nu54arALYYY/qMMaeBkwwFvHI709xFZUs3+Tr+fMLuWp3DvORIvrvlCJ29/VaXo5Tf8STQ9wBzRSRHREKAm4Et57T5A0NX54hIAkNdMHoHa5iCkkZgaN1vNTFOu43/+PgizjR38dPXCq0uRym/M26gG2P6gXuBV4BjwPPGmCMi8qCIXO9u9grQICJHgdeBbxhjGnxVdCDaW9pEeIid+Sm6INdkXJwdxyeXpfPEW8Wcqmmzuhyl/IpHfejGmK3GmFxjzGxjzH+6n3vAGLPF/dgYY75mjMkzxlxgjNnsy6IDUUFJE0syY3DYdS7XZN1/7XxmhDr41u8PMzioe5AqdZamyxRo6+7jeHWrDlf0kviIUL513QJ2lzSyaU+Z1eUo5Tc00KfA/rKhBbl0QpH33JSfzqrZ8Xx/63GqW3TxLqVAA31KFJQ0YhNYolvOeY2I8N83XkDvwCDf/uNhjNGuF6U00KdAQWkTC2ZGERHqsLqUoJIVP4OvXZ3Lq0dr+MvhaqvLUcpyGug+1jcwyP6yZh2u6CN3X5rDwtQoHthyhJbOPqvLUcpSGug+dqyqla6+Ad0Q2kccdhsPfeJCGjt6+e+Xdd10Nb1pH4CPFZS4F+TSG6IeeW7XxEatrJ4dz+Y95YSHOJiTFPGB47euyJxsaUr5Pb1C97GC0kbSYsKYGa0LcvnSFfOTSYgI4cV9FXT3DVhdjlKW0ED3IWMMBSVNXKxX5z4X4rDxyWUZtHT18eeDVVaXo5QlNNB9qLyxi9q2HpbpDdEpkRkXztp5iewra+JoZavV5Sg15TTQfWjn6aHlbJZroE+ZK+YnMTPaxe8PnKG9R1dkVNOLBroP7SxuIH5GCLnJH7xJp3zDYbNx07IMuvsG+MP+MzrhSE0rGug+YoxhZ1EDK2fF64YWUywl2sXVC5I5WtXKgfJmq8tRaspooPtIeePQhhYrZ2l3ixUunZtAVnw4fzpYSVNHr9XlKDUlNNB9ZEdxPQArZ8VbXMn0ZBPhpmUZGAOb9pTR2z9odUlK+ZwGuo/sLG4kISJkxEkuamrEzQjhE0vTqWjq4r+26ixSFfw00H3AGMOOogZWaP+55RalRbN6djxPbS9h6yEdn66Cmwa6D5Q2dFLd2q3dLX7imkUpLM6I4V9+d5CS+g6ry1HKZzwKdBFZLyInRKRQRO4bo90nRMSISL73Sgw8O4uHxp9fooHuFxw2G498ZikOu/ClX+/TpQFU0Bo30EXEDjwCXAvkAbeISN4I7SKBrwC7vF1koNle1EBiZCizE2dYXYpyS4sJ4+FPXcTRqla+96cjVpejlE94coW+HCg0xhQbY3qBzcANI7T7d+AhYFrvBzY4aHi7sJ5L5yRo/7mfuWJ+Ml9aN5tNu8t5dkeJ1eUo5XWeBHoaUD7s6wr3c+8RkaVAhjHmpbFeSEQ2iEiBiBTU1dWdd7GB4GhVK40dvVw2N8HqUtQIvv6heVw5P4nv/ukob5+qt7ocpbxq0jdFRcQGPAx8fby2xpjHjTH5xpj8xMTEyb61X9rmDolL52ig+yO7TfjxzYuZkxjBl369l6K6dqtLUsprPAn0M0DGsK/T3c+dFQksAt4QkRJgJbBlut4Y3XaqjvkpkSRFuawuRY0i0uVk4x35hDhs3PHkbmpbp3UvoQoingT6HmCuiOSISAhwM7Dl7EFjTIsxJsEYk22MyQZ2AtcbYwp8UrEf6+odoKCkSbtbAkBGXDhP3nkxjR293PGrPbR2636kKvCNG+jGmH7gXuAV4BjwvDHmiIg8KCLX+7rAQLLrdAO9A4NcNjc4u5OCzYXpMTx62zJO1bSx4ZkCHc6oAp5He4oaY7YCW8957oFR2q6bfFmBadupekIcNpbn6IJc/masvUpvXJrObwvK+ehP3+azK7Nw2M/v1pLuV6r8hc4U9aJtp+pYnh2Hy2m3uhR1HhZnxPDxJWmcqm1n0+4y+gd1IS8VmDTQveRMcxcna9pZk6v954EoPzuOj16UyrHqNn69s4y+AQ11FXg00L3ktWM1wNDkFRWYLpkVz8cWp3Gypo1ndpTokrsq4Gige8nfjtWSHR+u0/0D3PKcOD65LJ3iug42vl2s+5KqgKKB7gUdPf3sKGrgygXJOt0/CCzJjOW2lVnUtHbzizeLaGjvsbokpTyige4F207V0zswyJULkqwuRXnJgplR3L06h66+AR59s0hnlKqAoIHuBX8/VkOky8HF2TpcMZhkxs/gi2tnExHq4Mm3T/P2qTqMMVaXpdSoNNAnaXDQ8PqJWtbNS8J5nuOXlf9LiAjlnrWzyUuNYuvhan5TUK43S5Xf0gSapAMVzdS393KVdrcErVCnnVuXZ/KhvGQOVbTwmParKz+lgT5JrxyuxmET1uVqoAczEWHdvCTuWJVNS1cfP3u9kL2lTdoFo/yKBvokGGP488EqLp2bQHS40+py1BTITY7k3ivmMDM6jBf2VfDc7jIaO3qtLkspQAN9Ug6UN3OmuYuPXJhqdSlqCsWGh/C5y3JYvzCF41VtXPPjt3j9RK3VZSmlgT4ZLx2sIsRu4+o8nR063dhEWJObyD3rZhMb7uSuX+3hvhcO0typV+vKOh6ttqg+aHDQ8NKhKtbkJhAdpt0t01VqTBhb7r2UH716ko1vn+Zvx2r49kfyuP6i1Gk5yWysVS0nS1e1HJ9eoU/Q/vImqlq6+fCFM60uRVnM5bRz/3UL2HLvatJiw/nK5gPc/uRuShs6rC5NTTMa6BP0p3erCHHYuGqBdreoIQtTo3nxnlU8eMNC9pc186EfvcXDfz1Bh64Ho6aIBvoE9A0M8ueDlVwxL4lIl3a3qP9ltwm3X5LN3762lg8tTOEnrxVy+f99g+cLyhkY1CGOyrc00Cfg78dqqW/v5ab8dKtLUX4qJdrFT29Zwgv3rCItNox/+d1BPvrTt9leWG91aSqIeRToIrJeRE6ISKGI3DfC8a+JyFEROSgifxeRLO+X6j+eLygnKTKUtbm6d6ga27KsWF68ZxX/c/NiWrr6uHXjLm7buIu9pY1Wl6aC0LiBLiJ24BHgWiAPuEVE8s5pth/IN8ZcCPwO+IG3C/UX1S3dvHGilpvy089770k1PYkINyxO4+9fX8u3rlvAsapWPvHoDu54cjcHyputLk8FEU+GLS4HCo0xxQAishm4ATh6toEx5vVh7XcCt3mzSH/ywr4KBg18Kj/D6lJUgHE57Xx+zSw+szKTZ3aU8os3i/jYI++wbl4iX1gzm5Wz4t431FGHAKrz5cklZhpQPuzrCvdzo7kbeHmkAyKyQUQKRKSgrq7O8yr9xOCg4fmCclbOiiMrXncmUhMTHuLgi2tns+2bV/CNa+ZxqKKFW57YyfU/e4ct71bSr/uZqgny6sQiEbkNyAfWjnTcGPM48DhAfn5+wN3yf7uwntKGTr561VyrS1FBICLUwZcvn8Pdl+bw4r4zbNxWzD9t2s9DMWHcsSoLG0J4qM79U57z5KflDDC8fyHd/dz7iMhVwLeAtcaYoFxb9IltxSRFhnLdBTqZSHmPy2nn1hWZ3HxxBq8dr+XxbcX819bjOGzCorRoVuTEkRkXPi1nnqrz40mg7wHmikgOQ0F+M3Dr8AYisgT4BbDeGBOUqxQdrWxl26l6vrl+PqEOu9XlqCBkswlX5SVzVV4yx6tb+e6WI+wva+ZAeTMpUS6WZcVyUUYMEXrVrkYx7k+GMaZfRO4FXgHswJPGmCMi8iBQYIzZAvwQiAB+676KKDPGXO/Duqfcxm3FzAix680kNSXmp0Rx/UVpXLMwhYMVLew+3chLh6p4+XAVc5MiWZIZw4KZUbpLlnofj/5Xb4zZCmw957kHhj2+yst1+ZWqli62vFvJ7Zdk60JcakqFOuxcnB3Hxdlx1LR2c6C8mf1lTZzY00aow8YFadEsyYwlKz4cm3bJTHv6u5sHNm47jQHuWp1tdSnKD/lyeOFwyVEurlmYwtV5yRTXdbC/rImDFS0UlDYRHeZkUWoUF6RFkx6n4T5daaCPo6Kpk2d3lPLxJWlkxIVbXY5S2ESYkxTBnKQIbugf5EhlC4fOtLDzdCPvFDW8F+4LZkaRFT8Du03DfbrQQB/Hj149BQJfuzrX6lKU+oAQh40lmbEsyYylu2+AY1Wt7wv3UIeNOUkR5CZHkpscqV2GQU4DfQzHq1t5cX8FGy6bRWpMmNXlKDUml9P+Xrj39A1QVNfOiZp2Tta0caSyFYDYcCfpseF09vazJDOWhalRuJwTG7VljKGps4+a1m5qWrupbe3hteM1tHb309bVR2t3P529/QwMGgYMOGxCiN1GWIid6DAnMeFOkiNdpES7SI5y6W8SXqCBPoaHXj5OZKiDe9bNtroUpc5LqNNOXmo0eanRGGOoae3hVG0b5Y2dlDV28h8vHQPAJkO7LmXFh5Mc5SIhIpToMCehDhsOm9DVN0hnbz8dPQN09vbT2t1HTWvPewHeO8Ks1vAQO1EuJ1FhDpIiQ7HbBJsI/YOG3oFBOnv6qWzu4lhVK/3uJYVDHDay48OZkxhBXmo0cTNCpvTvK1hooI9i66EqXj9Rx79eN5+YcP3hUoFLREiJHroSPuuqBUnsL2/mSGM0WNMAAAmWSURBVGUrpQ0dlDR0UlLcSF17D739g+d8P8wIcRAeYifC5SA50sXF2XEkRYWSHDl0dZ0SHUpSpIvXjtd6PJRyYNDQ0N5DVUs3JQ0dFNd1sLWmmq2Hq0mNdrEkM5almbGEhei8D09poI+gqaOXB/54mAvSovmH1TlWl6OU1yW5R8xcszDlfc8bM3QV3ds/SN+AIcxpx+W0eTxL9XzGxdttQlKUi6QoFxdlxADQ2NH73k3elw5V8cqRai5Mj2Z5TjzGGJ0tOw4N9BE8+OejNHf28ezdK3SJXDWtiAihDrtls6HjZoRw2dxELpubSGVzF7tLGjlQ3sy+smbePFnHF9fO4sMXzNR/l6PQv5VzvHyoit/vP8OXL5/DgplRVpej1LSVGhPGxxancf/6+dywOJX+gUG+svkAVz78Jpt3l32ga0hpoL/P8epWvv7bd1mcEcOXL59jdTlKKYZu8K7IieeVr67hsduWEeVyct+Lh1j7w9f51Tun6eodsLpEv6GB7tbU0cvnnykgItTBLz67jBCH/tUo5U9sNmH9ohS23Luap/9hORmx4XzvT0e57Aev8fM3Cmnr7rO6RMtpHzrQ0dPPF57dS01LD7/5wkqSo1zjf5NSyhIiwtrcRNbmJrL7dCM/e72QH/zlBI+9UcSdq7K5a3UOsdN02OO0D/TW7j7u+tUeDpQ38+NPL2ZJZqzVJSmlPLQ8J45ncpZzsKKZR14v5CevFbLx7dN8ZkUmn79sFknT7OJsWgd6bVs3n3+6gCOVrfzsliVcqxtXKBWQLkyP4RefzedkTRs/f72QX759mqe3l/LRi1K5c1U2F6RHW13ilJi2gb69qJ5/2nSA9p4+Hr1tGVfnJVtdklJqknKTI/nxzUv456tz2bjtNC/sq+CFfRUsy4rlzlXZrF+UEtRryE+7QG/r7uNnrxXyxLZishNm8OvPrWBeSqTVZSmlvCgrfgb//rFFfGP9PH5bUMEzO0r4x037SYgI5SMXzuSGxakszogJuolK0ybQu/sGeHHfGR5+9ST17T18Kj+d73x0ITN0Oy+lglaUy8ndl+Zw16ps3jhZy/N7KnhudxlPbS8hMy6cj140k2sXzSRvZhS2IFgcLOjTrLC2nT/sP8Nzu8to7OhlSWYMG+/IZ7F7qrFSKvjZbMIV85O5Yn4yrd19vHK4mi3vVvLoG0U88noRseFOLpkdz6rZCayek0B2fGBuyu1RoIvIeuB/GNpTdKMx5vvnHA8FngGWAQ3Ap40xJd4tdXzGGCpbujlQ1sze0ibeOFlLcV0HInDVgmTuXJXNqtnxAflBKaW8I8rl5Kb8DG7Kz6CurYdtp+p4p7CB7UX1bD1UDQwtMzw/JYr5MyNZkBLFvJRIMuPCiQl3+nV+jBvoImIHHgGuBiqAPSKyxRhzdFizu4EmY8wcEbkZeAj4tC8Krm7pZl9ZEw3tPdS199LQ3kNDey9VLV0U1XXQ3tMPQKjDRn720I2QD+WlvG+lOaWUAkiMDOXGpencuDQdYwyn6zvYXtTAkcoWjlW1sXl3OV19/zsTNcxpZ2aMi9ToMJKjXMSEO4kOcxLlchAd7iQi1EmIw4bTLoQ6bITY7YiAMTBojPsPJEeFkh7r/R3QPLlCXw4UGmOKAURkM3ADMDzQbwC+6378O+BnIiLGGOPFWgHYW9rEl5/bx1AtEBseQkJECEmRLj6xNI3ZSRFclD60I7rO9lRKeUpEmJUYwazEiPeeGxw0lDV2cry6jTPNXVQ2d1HV0kVlczdFRfW0dPXROYGlB764djb3XTvfm+UDngV6GlA+7OsKYMVobYwx/SLSAsQD9cMbicgGYIP7y3YROTHKeyac+72jKfGkkX/y+BwDnJ6nH/rMxL7N0nOcYM0T4fPzvP8huH/i35412oEpvSlqjHkceHy8diJSYIzJn4KSLDMdzhH0PIPJdDhHCOzz9KRP4gyQMezrdPdzI7YREQcQzdDNUaWUUlPEk0DfA8wVkRwRCQFuBrac02YLcIf78SeB13zRf66UUmp043a5uPvE7wVeYWjY4pPGmCMi8iBQYIzZAvwSeFZECoFGhkJ/MsbtlgkC0+EcQc8zmEyHc4QAPk/RC2mllAoOOq5PKaWChAa6UkoFCcsDXUTiRORVETnl/u+IO0yIyICIHHD/OfemrN8SkfUickJECkXkvhGOh4rIb9zHd4lI9tRXOXkenOedIlI37DP8nBV1ToaIPCkitSJyeJTjIiI/cf8dHBSRpVNd42R5cI7rRKRl2Of4wFTX6A0ikiEir4vIURE5IiJfGaFN4H2exhhL/wA/AO5zP74PeGiUdu1W1zqBc7MDRcAsIAR4F8g7p82XgMfcj28GfmN13T46zzuBn1ld6yTPcw2wFDg8yvHrgJcBAVYCu6yu2QfnuA74s9V1euE8ZwJL3Y8jgZMj/MwG3Odp+RU6Q8sGPO1+/DTwMQtr8bb3lk0wxvQCZ5dNGG74+f8OuFL8efWfkXlyngHPGPMWQ6O4RnMD8IwZshOIEZGA2gbLg3MMCsaYKmPMPvfjNuAYQzPehwu4z9MfAj3ZGFPlflwNjLZ1kEtECkRkp4gESuiPtGzCuT8071s2ATi7bEIg8eQ8AT7h/tX1dyKSMcLxQOfp30Ogu0RE3hWRl0VkodXFTJa7m3MJsOucQwH3eU7J1H8R+RuQMsKhbw3/whhjRGS0cZRZxpgzIjILeE1EDhljirxdq/KZPwGbjDE9IvIFhn4rucLimtT528fQv8V2EbkO+AMw1+KaJkxEIoAXgK8aY1qtrmeypiTQjTFXjXZMRGpEZKYxpsr960ztKK9xxv3fYhF5g6H/o/p7oJ/PsgkVAbxswrjnaYwZfk4bGbp3Emw8+bwD2vDQM8ZsFZGfi0iCMSZgFiY7S0ScDIX5r40xL47QJOA+T3/ochm+bMAdwB/PbSAise5NNBCRBGA171++119Nl2UTxj3Pc/oer2eozzLYbAFud4+OWAm0DOtODAoiknL2Ho+ILGcoQwLtAgT3OfwSOGaMeXiUZgH3efrDFnTfB54XkbuBUuBTACKSD3zRGPM5YAHwCxEZZOgH6Pvm/Rts+CVjzbIJU87D8/wnEbke6GfoPO+0rOAJEpFNDI3ySBCRCuA7gBPAGPMYsJWhkRGFQCdwlzWVTpwH5/hJ4B4R6Qe6gJsD8AIEhi4KPwscEpED7uf+FciEwP08deq/UkoFCX/oclFKKeUFGuhKKRUkNNCVUipIaKArpVSQ0EBXSqkgoYGulFJBQgNdKaWCxP8HpM5WoWUETOgAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "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",
        "colab": {}
      },
      "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)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RH1u68Hqk6BZ",
        "colab_type": "code",
        "outputId": "c830d06e-c0e5-4608-8800-54e750076f91",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "sample1.head()"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<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>-0.179278</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.236714</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.255502</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>-0.029321</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.004818</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   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"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3xHXTlTdk511",
        "colab_type": "code",
        "outputId": "b4295e59-b0ff-4a0b-f8ee-26cebd1135d3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 204
        }
      },
      "source": [
        "sample2.head()"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
              "    }\n",
              "\n",
              "    .dataframe tbody tr th {\n",
              "        vertical-align: top;\n",
              "    }\n",
              "\n",
              "    .dataframe thead th {\n",
              "        text-align: right;\n",
              "    }\n",
              "</style>\n",
              "<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>0.680541</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>1</td>\n",
              "      <td>0.436810</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>2</td>\n",
              "      <td>0.604089</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>3</td>\n",
              "      <td>0.518702</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>4</td>\n",
              "      <td>0.479711</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   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"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yIvOH3yWiTU9",
        "colab_type": "text"
      },
      "source": [
        "Find the parameters required to compute the T statistic"
      ]
    },
    {
      "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 = sample2[1].shape[0]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3i3gxyQziXD5",
        "colab_type": "text"
      },
      "source": [
        "## Find the degrees of freedom to get the critical value\n",
        "$$df = \\frac{\\left(\\frac{s_1^2}{n_1} + \\frac{s_2^2}{n_2}\\right)^2}{\\frac{\\left(\\frac{s_1^2}{n_1}\\right)^2}{n_1 - 1}+ \\frac{\\left(\\frac{s_2^2}{n_2}\\right)^2}{n_2 - 1}}$$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "p4Hx9UL3flF8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "df = np.square((s1/n1) + (s2 / n2)) / (((s1/n1)**2)/(n1-1) + ((s2/n2)**2)/(n2-1))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "nyai_S1zihfm",
        "colab_type": "text"
      },
      "source": [
        "Compare the critical value and the T statistic and conclude whether null hypothesis is accepted or not. Print 'YES' is it is rejected, otherwise print 'NO'. \n",
        "Critical value is given by $t_{1-\\alpha/2,df}$. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ST8J42mAfn0R",
        "colab_type": "code",
        "outputId": "7dbf17d9-f177-48f7-e879-b154f26f1a19",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "T = (mu1 - mu2) / np.sqrt((s1/n1) + (s2 / n2))\n",
        "critical_value = stats.t.pdf((1-significance)/2,df)\n",
        "if np.abs(T) > critical_value:\n",
        "  print('YES')\n",
        "else:\n",
        "  print('NO')"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "YES\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SrOP9BwSiwVc",
        "colab_type": "text"
      },
      "source": [
        "Plot the distribution of both the samples to visualize"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "omfVDZqxfyAM",
        "colab_type": "code",
        "outputId": "ec293ed6-04e5-4dae-8e44-61dcc8ee8395",
        "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": 13,
      "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": []
    }
  ]
}