Modeling_data_distributions.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "collapsed_sections": []
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "Task:\n",
        "- Implement a uniform distribution number generator. To test the hypothesis about the uniformity of the distribution.\n",
        "- On the basis of a uniform distribution, make a normal distribution. To test the hypothesis of the normality of the distribution.\n",
        "- To make a sample from the values of Kolmogorov statistics for 100 simulated normal distributions."
      ],
      "metadata": {
        "id": "hN0Z8qtmY8em"
      }
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "id": "3oATSCzl0GKj"
      },
      "outputs": [],
      "source": [
        "import random\n",
        "import pandas as pd\n",
        "import matplotlib.pyplot as plt\n",
        "import numpy as np\n",
        "from scipy import stats"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "- m, module; 0 < m; \n",
        "- а, multiplier; 0 < а < m; \n",
        "- с, increment; 0 < с < m;  \n",
        "- X(0), initial value; 0 =< X(0) < m. \n",
        "\n",
        "The desired sequence of random numbers: \n",
        "X(n+i) = (а*Х(n) + с) mod m, n >= 0.  "
      ],
      "metadata": {
        "id": "0VX-kWqhTm7d"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "def generate(m, a, c, x_start, number):\n",
        "    gen_list = [x_start]\n",
        "    x_prev = x_start\n",
        "    for elt in range(number-1):\n",
        "        x_prev = (a*x_prev+c)%m\n",
        "        gen_list.append(x_prev)\n",
        "    return gen_list"
      ],
      "metadata": {
        "id": "LYExXTSIUWrR"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Example with bad params in function \"geterate\""
      ],
      "metadata": {
        "id": "4rUUFZBRaBrx"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "N = 100\n",
        "n = range(N)\n",
        "l1 = np.array(generate(10, 7, 7, 7, 100))/10\n",
        "plt.figure(figsize=(15, 7))\n",
        "\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(n, l1, '.')\n",
        "plt.title('Distrubution u1');"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "CxohqorhZNJK",
        "outputId": "9c78d732-14d2-4bbd-cda2-34e94ccc4eea"
      },
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x504 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Example with suitable params in function \"geterate\""
      ],
      "metadata": {
        "id": "TkKePTPBaKTm"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "N = 100\n",
        "n = range(N)\n",
        "random.seed(17)\n",
        "u1 = np.array(generate(16807, 0x7fffffff, 0, 7, N))/16807\n",
        "u2 = np.array(generate(16807, 0x7fffffff, 0, 5, N))/16807\n",
        "\n",
        "plt.figure(figsize=(15, 7))\n",
        "\n",
        "plt.subplot(1,2,1)\n",
        "plt.plot(n, u1, '.')\n",
        "plt.title('Distrubution u1')\n",
        "plt.subplot(1,2,2)\n",
        "plt.plot(n, u2, '.')\n",
        "plt.title('Distrubution u2')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 444
        },
        "id": "JaJpLTxt3HNd",
        "outputId": "014fcf0b-2bf0-4d55-e96a-276c317268e4"
      },
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 1080x504 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "stats.kstest(u1, \"uniform\") "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xvntI55fhfro",
        "outputId": "0b2724be-4940-41e0-fcc9-71888fe1243c"
      },
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KstestResult(statistic=0.06560599750104124, pvalue=0.7574460367157285)"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "stats.kstest(u2, \"uniform\") "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DKsaKu9z8Pi7",
        "outputId": "a9fe6bb0-b050-424b-8e25-a8474862c51b"
      },
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KstestResult(statistic=0.0768411971202475, pvalue=0.5696779015482883)"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "u11 = pd.Series(u1)\n",
        "u11.hist();"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "bEMBylu3d7t_",
        "outputId": "ba44ffea-3cb3-48d0-cab2-a29b55487713"
      },
      "execution_count": 7,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Modeling of the normal distribution using a uniform distribution"
      ],
      "metadata": {
        "id": "gJweTXbMaajK"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "X_norm = np.sqrt(-2*np.log(u1))*np.cos(2*np.pi*u2)\n",
        "Y_norm = np.sqrt(-2*np.log(u1))*np.sin(2*np.pi*u2)\n",
        "plt.hist(X_norm, label = 'X');\n",
        "plt.hist(Y_norm, label = 'Y');\n",
        "plt.legend();"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "NxAv13q67K6U",
        "outputId": "ce885337-04c0-453d-9679-9033029b5e17"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.plot(X_norm, Y_norm, '.')\n",
        "plt.xlabel('X');\n",
        "plt.ylabel('Y');"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 278
        },
        "id": "FIKAuUvqpzvi",
        "outputId": "4e77b3ac-0c18-4e2d-d155-83aeca8b83e4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "stats.kstest(X_norm, \"norm\") "
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "i9PHlEqHfw3X",
        "outputId": "0598c33f-b87c-4d92-a0d1-c0fd9e0bd59f"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KstestResult(statistic=0.05511366112990257, pvalue=0.9216707027895396)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Making a new sample of 100 values of the Kolmogorov normality test"
      ],
      "metadata": {
        "id": "Zcm4OTTma97_"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "import statistics\n",
        "from scipy.stats import norm\n",
        "N = 100\n",
        "n = range(N)\n",
        "statistics_list = []\n",
        "for i in range(1,N*2+1,2):\n",
        "  u1 = np.array(generate(16807, 0x7fffffff, 0, i, N))/16807\n",
        "\n",
        "  u2 = np.array(generate(16807, 0x7fffffff, 0, i+1, N))/16807\n",
        "  X_norm = np.sqrt(-2*np.log(u1))*np.cos(2*np.pi*u2)\n",
        "  st, p = stats.kstest(X_norm, 'norm')\n",
        "  statistics_list.append(st)"
      ],
      "metadata": {
        "id": "_RnjBDuFxvYA"
      },
      "execution_count": 10,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "plt.hist(statistics_list, bins = 30, density = True);"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "LO5ghSKuzIRa",
        "outputId": "e20e1720-eae4-48af-e3d4-d75f354cfb0c"
      },
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": "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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**This sample has a Kolmogorov distribution**"
      ],
      "metadata": {
        "id": "Ont2w7gec0xb"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "#Chi square test implementation and checking the distribution"
      ],
      "metadata": {
        "id": "glJ9xKL1NN5Z"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import kstwobign\n",
        "import statistics\n",
        "\n",
        "K = len(statistics_list)\n",
        "\n",
        "m=statistics.mean(statistics_list)\n",
        "std_1=statistics.stdev(statistics_list)\n",
        "pmax=max(statistics_list);\n",
        "pmin=min(statistics_list);\n",
        "dis=(pmax-pmin)/4;\n",
        "num=[0]*5\n",
        "\n",
        "i=0;\n",
        "while i<5:\n",
        "  for j in range(i, K):\n",
        "    if (statistics_list[j]>=pmin) and (statistics_list[j]<pmin+dis):\n",
        "      num[i]=num[i]+1\n",
        "  pmin=pmin+dis\n",
        "  i=i+1\n",
        "\n",
        "pmin=min(statistics_list);\n",
        "\n",
        "F = [0]*5\n",
        "F[0]=kstwobign.cdf(pmin,m,std_1)\n",
        "F[1]=kstwobign.cdf(pmin+dis,m,std_1)\n",
        "F[2]=kstwobign.cdf(pmin+2*dis,m,std_1)\n",
        "F[3]=kstwobign.cdf(pmin+3*dis,m,std_1)\n",
        "# F[4]=kstwobign.cdf(pmin+4*dis,m,std_1)\n",
        "F[4]=kstwobign.cdf(pmax,m,std_1)\n",
        "\n",
        "\n",
        "p = [0]*5\n",
        "p[0] = F[0]\n",
        "for i in range(1,4):\n",
        "  p[i]=F[i]-F[i-1]\n",
        "p[4] = 1 - F[4]\n",
        "\n",
        "k = 0\n",
        "for i in range(5):\n",
        "  k = k+((num[i]-K*p[i])**2)/(K*p[i])\n",
        "print('The chi square value is ', k)"
      ],
      "metadata": {
        "id": "mulWFTWgIUUn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "81f8b968-79e7-465b-e392-0b9d33bbcfed"
      },
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "The chi square value is  inf\n"
          ]
        },
        {
          "output_type": "stream",
          "name": "stderr",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:40: RuntimeWarning: divide by zero encountered in double_scalars\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Here I get a mistake"
      ],
      "metadata": {
        "id": "LcJZADsviqZa"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "p"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mp93LgcvoPa7",
        "outputId": "1fcb7324-8a1b-40c2-9c15-31c67bcae8f2"
      },
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[0.0, 0.0, 0.0028753263907296107, 0.9777218085921773, 1.6912351806785964e-06]"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "sum(p)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rInyFmkdg_SU",
        "outputId": "c3a6aa68-8b95-4d99-92dc-4523da252bc4"
      },
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.9805988262180876"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "num"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wp24Zqw8g_VH",
        "outputId": "ebf06049-e914-4c38-fb92-edff8f4a1049"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "[25, 44, 20, 8, 1]"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "stats.kstest(statistics_list, 'norm')"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rJJodCWMiKyz",
        "outputId": "ac4450db-a66b-4c2a-af97-1262b9da4ca4"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "KstestResult(statistic=0.7109458139539231, pvalue=1.656218397731384e-51)"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    }
  ]
}