08_Distributions.ipynb

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        "<a href=\"https://colab.research.google.com/github/GustavoBD-Dev/AnalyticalModelsWithPythonCourse/blob/Session-3/08_Distributions.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "#**Distribuciones de probabilidad**"
      ],
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      "source": [
        "Las distribuciones de probabilidad describen cómo se distribuyen los valores de una variable aleatoria. En análisis de datos y modelos analíticos, entender estas distribuciones es crucial para hacer inferencias y tomar decisiones basadas en datos.\n",
        "\n",
        "####**Distribución Uniforme**\n",
        "\n",
        "1. **Distribución Uniforme Discreta**\n",
        "- **Descripción:** Todos los valores posibles tienen la misma probabilidad de ocurrencia.\n",
        "- **Fórmula:** P(X = x) = 1 / n, donde n es el número total de posibles valores.\n",
        "- **Ejemplo:**\n",
        "     ```python\n",
        "     import numpy as np\n",
        "     valores = np.arange(1, 7)  # Dados de seis caras\n",
        "     probabilidades = np.ones(6) / 6\n",
        "     print(\"Valores:\", valores)\n",
        "     print(\"Probabilidades:\", probabilidades)\n",
        "     ```\n",
        "- **Interpretación:** En el lanzamiento de un dado justo de seis caras, cada cara tiene una probabilidad de 1/6.\n",
        "- **Consideración:** Útil en situaciones donde todos los eventos son igualmente probables.\n",
        "\n",
        "2. **Distribución Uniforme Continua**\n",
        "- **Descripción:** La probabilidad está uniformemente distribuida en un intervalo continuo [a, b].\n",
        "- **Fórmula:** f(x) = 1 / (b - a) para a <= x <= b.\n",
        "- **Ejemplo:**\n",
        "     ```python\n",
        "     a, b = 0, 1\n",
        "     muestra = np.random.uniform(a, b, 1000)\n",
        "     ```\n",
        "- **Interpretación:** Cada valor en el intervalo tiene la misma probabilidad de ocurrir.\n",
        "- **Consideración:** Utilizada en simulaciones y análisis donde se asume que todos los valores en un rango son igualmente probables.\n",
        "\n",
        "####**Distribución Normal**\n",
        "\n",
        "- **Descripción:** Describe datos que se distribuyen de manera simétrica alrededor de la media, formando una \"campana\" (curva de Gauss).\n",
        "- **Fórmula:** f(x) = (1 / (desviación estándar * raíz cuadrada de 2 * pi)) * e^(-(x - media)^2 / (2 * desviación estándar^2)).\n",
        "- **Ejemplo:**\n",
        "  ```python\n",
        "  import matplotlib.pyplot as plt\n",
        "  media, desviacion_estandar = 0, 1\n",
        "  muestra = np.random.normal(media, desviacion_estandar, 1000)\n",
        "  plt.hist(muestra, bins=30, density=True)\n",
        "  plt.show()\n",
        "  ```\n",
        "- **Interpretación:** La mayoría de los valores están cerca de la media, y la probabilidad disminuye simétricamente a medida que se alejan de ella.\n",
        "- **Consideración:** Muchas variables naturales y de comportamiento siguen una distribución normal.\n",
        "\n",
        "####**Distribución Binomial**\n",
        "\n",
        "- **Descripción:** Describe el número de éxitos en una secuencia de n ensayos de Bernoulli independientes, cada uno con probabilidad de éxito p.\n",
        "- **Fórmula:** P(X = k) = (n sobre k) * p^k * (1 - p)^(n - k).\n",
        "- **Ejemplo:**\n",
        "  ```python\n",
        "  from scipy.stats import binom\n",
        "  n, p = 10, 0.5\n",
        "  x = np.arange(0, n + 1)\n",
        "  probabilidades = binom.pmf(x, n, p)\n",
        "  plt.bar(x, probabilidades)\n",
        "  plt.show()\n",
        "  ```\n",
        "- **Interpretación:** Utilizada para modelar el número de éxitos en un número fijo de ensayos independientes.\n",
        "- **Consideración:** Aplicable en situaciones con dos posibles resultados (éxito o fracaso) en cada ensayo.\n",
        "\n",
        "####**Distribución de Poisson**\n",
        "\n",
        "- **Descripción:** Describe el número de eventos que ocurren en un intervalo de tiempo o espacio fijo.\n",
        "- **Fórmula:** P(X = k) = (lambda^k * e^(-lambda)) / k!, donde lambda es el número promedio de eventos.\n",
        "- **Ejemplo:**\n",
        "  ```python\n",
        "  from scipy.stats import poisson\n",
        "  lambda_ = 5\n",
        "  x = np.arange(0, 15)\n",
        "  probabilidades = poisson.pmf(x, lambda_)\n",
        "  plt.bar(x, probabilidades)\n",
        "  plt.show()\n",
        "  ```\n",
        "- **Interpretación:** Utilizada para modelar eventos raros en un intervalo fijo.\n",
        "- **Consideración:** Apropiada cuando los eventos ocurren independientemente y la tasa de ocurrencia es constante.\n",
        "\n",
        "###**Ejemplo**\n",
        "\n",
        "Consideremos una empresa que analiza el tiempo de espera en una fila:\n",
        "\n",
        "```python\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Distribución uniforme continua\n",
        "a, b = 5, 15\n",
        "muestra_uniforme = np.random.uniform(a, b, 1000)\n",
        "plt.hist(muestra_uniforme, bins=30, density=True, alpha=0.5, color='g')\n",
        "plt.title('Distribución Uniforme Continua')\n",
        "plt.show()\n",
        "\n",
        "# Distribución normal\n",
        "media, desviacion_estandar = 10, 2\n",
        "muestra_normal = np.random.normal(media, desviacion_estandar, 1000)\n",
        "plt.hist(muestra_normal, bins=30, density=True, alpha=0.5, color='b')\n",
        "plt.title('Distribución Normal')\n",
        "plt.show()\n",
        "\n",
        "# Distribución binomial\n",
        "from scipy.stats import binom\n",
        "n, p = 10, 0.5\n",
        "x = np.arange(0, n + 1)\n",
        "probabilidades_binomiales = binom.pmf(x, n, p)\n",
        "plt.bar(x, probabilidades_binomiales, alpha=0.5, color='r')\n",
        "plt.title('Distribución Binomial')\n",
        "plt.show()\n",
        "\n",
        "# Distribución de Poisson\n",
        "from scipy.stats import poisson\n",
        "lambda_ = 5\n",
        "x = np.arange(0, 15)\n",
        "probabilidades_poisson = poisson.pmf(x, lambda_)\n",
        "plt.bar(x, probabilidades_poisson, alpha=0.5, color='y')\n",
        "plt.title('Distribución de Poisson')\n",
        "plt.show()\n",
        "```\n",
        "\n",
        "###**Consideraciones:**\n",
        "\n",
        "- **Distribución Uniforme:** Útil en situaciones donde todos los resultados son igualmente probables. Es sencilla pero rara en la práctica real.\n",
        "- **Distribución Normal:** Frecuente en datos naturales y de comportamiento. Importante en estadística debido al teorema central del límite.\n",
        "- **Distribución Binomial:** Adecuada para experimentos con dos posibles resultados (éxito o fracaso). Útil en encuestas y estudios clínicos.\n",
        "- **Distribución de Poisson:** Ideal para modelar eventos raros en intervalos de tiempo o espacio. Útil en telecomunicaciones y biología."
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      "source": [
        "##**Ejercicios**"
      ],
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      "source": [
        "###**Ejercicio 1: Distribución Normal**\n",
        "**Objetivo:** Calcula la media y la desviación estándar de una columna del DataFrame y ajusta una distribución normal. Grafica el histograma de la columna y la distribución normal ajustada."
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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "from scipy.stats import norm\n",
        "\n",
        "# Ejemplo con la columna 'ROA(C) before interest and depreciation before interest'\n",
        "data = df[' ROA(C) before interest and depreciation before interest'].dropna()\n",
        "mean, std_dev = np.mean(data), np.std(data)\n",
        "\n",
        "# Graficar histograma y distribución normal ajustada\n",
        "plt.hist(data, bins=30, density=True, alpha=0.6, color='g')\n",
        "\n",
        "xmin, xmax = plt.xlim()\n",
        "x = np.linspace(xmin, xmax, 100)\n",
        "p = norm.pdf(x, mean, std_dev)\n",
        "plt.plot(x, p, 'k', linewidth=2)\n",
        "\n",
        "plt.title('Distribución Normal Ajustada')\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 2: Distribución Exponencial**\n",
        "**Objetivo:** Ajusta una distribución exponencial a una columna del DataFrame y grafica el histograma de los datos junto con la distribución exponencial ajustada."
      ],
      "metadata": {
        "id": "id_Dt-70EAjd"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import expon\n",
        "\n",
        "# Ejemplo con la columna 'Operating Expense Rate'\n",
        "data = df[' Operating Expense Rate'].dropna()\n",
        "loc, scale = expon.fit(data)\n",
        "\n",
        "# Graficar histograma y distribución exponencial ajustada\n",
        "plt.hist(data, bins=30, density=True, alpha=0.6, color='b')\n",
        "\n",
        "x = np.linspace(0, np.max(data), 100)\n",
        "p = expon.pdf(x, loc, scale)\n",
        "plt.plot(x, p, 'r', linewidth=2)\n",
        "\n",
        "plt.title('Distribución Exponencial Ajustada')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 471
        },
        "id": "5HOndWFcEAdB",
        "outputId": "fea8771c-4f53-4e8e-d199-e5f2cc48c618"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 3: Distribución de Poisson**\n",
        "**Objetivo:** Ajusta una distribución de Poisson a una columna que representa conteos y grafica el histograma con la distribución ajustada."
      ],
      "metadata": {
        "id": "CHyptY4iEAXX"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import drive\n",
        "drive.mount('/content/drive')\n",
        "from scipy.stats import poisson\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "url = 'https://drive.google.com/uc?id=13V1yuYcvuXfXGYL4lJHlPXNgI3MZDjVe'\n",
        "data = pd.read_csv(url, sep=',', on_bad_lines='warn')\n",
        "df = data\n",
        "# Ejemplo con la columna 'Revenue Per Share (Yuan Â¥)'\n",
        "data = df[' Revenue Per Share (Yuan ¥)'].dropna()\n",
        "mean = np.mean(data)\n",
        "\n",
        "# Graficar histograma y distribución de Poisson ajustada\n",
        "plt.hist(data, bins=30, density=True, alpha=0.6, color='c')\n",
        "\n",
        "x = np.arange(0, np.max(data) + 1)\n",
        "p = poisson.pmf(x, mean)\n",
        "plt.stem(x, p, 'r', linewidth=2)\n",
        "\n",
        "plt.title('Distribución de Poisson Ajustada')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8GFDUMzoEARn",
        "outputId": "1e6ea1fa-6346-4d73-c05e-cd56c435ee44"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 4: Distribución Binomial**\n",
        "**Objetivo:** Ajusta una distribución binomial a una columna que representa una tasa de éxito y grafica el histograma con la distribución binomial ajustada."
      ],
      "metadata": {
        "id": "sM2ugUohEAL4"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from scipy.stats import binom\n",
        "from google.colab import drive\n",
        "drive.mount('/content/drive')\n",
        "from scipy.stats import poisson\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "url = 'https://drive.google.com/uc?id=13V1yuYcvuXfXGYL4lJHlPXNgI3MZDjVe'\n",
        "data = pd.read_csv(url, sep=',', on_bad_lines='warn')\n",
        "df = data\n",
        "# Ejemplo con la columna 'Cash Flow Per Share'\n",
        "data = df[' Cash Flow Per Share'].dropna()\n",
        "n = len(data)  # Número de ensayos\n",
        "p = np.mean(data)  # Probabilidad de éxito\n",
        "\n",
        "# Graficar histograma y distribución binomial ajustada\n",
        "plt.hist(data, bins=30, density=True, alpha=0.6, color='m')\n",
        "\n",
        "x = np.arange(0, np.max(data) + 1)\n",
        "p = binom.pmf(x, n, p)\n",
        "plt.stem(x, p, 'r', linewidth=2)\n",
        "\n",
        "plt.title('Distribución Binomial Ajustada')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 779
        },
        "id": "IPAgBpJ8EAGZ",
        "outputId": "7399629d-de31-4224-855f-54ce55879554"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Drive already mounted at /content/drive; to attempt to forcibly remount, call drive.mount(\"/content/drive\", force_remount=True).\n"
          ]
        },
        {
          "output_type": "error",
          "ename": "TypeError",
          "evalue": "stem() got an unexpected keyword argument 'linewidth'",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-3-0eecb401e766>\u001b[0m in \u001b[0;36m<cell line: 22>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     20\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m \u001b[0mp\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mbinom\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpmf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 22\u001b[0;31m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstem\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mp\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'r'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlinewidth\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m2\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     23\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     24\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Distribución Binomial Ajustada'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/matplotlib/_api/deprecation.py\u001b[0m in \u001b[0;36mwrapper\u001b[0;34m(*inner_args, **inner_kwargs)\u001b[0m\n\u001b[1;32m    382\u001b[0m             \u001b[0;31m# Early return in the simple, non-deprecated case (much faster than\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    383\u001b[0m             \u001b[0;31m# calling bind()).\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 384\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0minner_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0minner_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    385\u001b[0m         \u001b[0marguments\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mbind\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0minner_args\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0minner_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marguments\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    386\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mis_varargs\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0marguments\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mTypeError\u001b[0m: stem() got an unexpected keyword argument 'linewidth'"
          ]
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 5: Distribución Gamma**\n",
        "Problema: Ajusta una distribución Gamma a una columna del DataFrame y grafica el histograma con la distribución Gamma ajustada."
      ],
      "metadata": {
        "id": "vYxD-TrsD__V"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "om1xjkvDD_6L"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 6: Distribución Beta**\n",
        "**Objetivo:** Ajusta una distribución Beta a una columna que contiene valores entre 0 y 1 y grafica el histograma con la distribución Beta ajustada."
      ],
      "metadata": {
        "id": "WVPF27t7D_zR"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "i8A8GZB1D_tT"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 7: Distribución de Cauchy**\n",
        "**Objetivo:** Ajusta una distribución de Cauchy a una columna del DataFrame y grafica el histograma con la distribución Cauchy ajustada."
      ],
      "metadata": {
        "id": "Od5C_A6MD_nj"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "9QDzLiG4D_hu"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 8: Distribución Log-Normal**\n",
        "**Objetivo:** Ajusta una distribución Log-Normal a una columna del DataFrame y grafica el histograma con la distribución Log-Normal ajustada."
      ],
      "metadata": {
        "id": "5tHvGJhdD_aa"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "VbTcxrU1D_TY"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "###**Ejercicio 9: Distribución Weibull**\n",
        "**Objetivo:** Ajusta una distribución Weibull a una columna del DataFrame y grafica el histograma con la distribución Weibull ajustada."
      ],
      "metadata": {
        "id": "CAJXwy7gD-6i"
      }
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "L8jheVB8D-ia"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}