Libro3_EstadisticaInferencial.ipynb

libro3_estadisticainferencial.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/gist/tannsr/4359e86ac4796ad863fc28f9171d8c9e/libro3_estadisticainferencial.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "Una estadística es una función de una muestra aleatoria que no depende de parámetros desconocidos."
      ],
      "metadata": {
        "id": "WL8hitQBqT3L"
      },
      "id": "WL8hitQBqT3L"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Una muestra aleatoria es una colección de variables aleatorias $X_1, . . . , X_n$ que son independientes e idénticamente distribui-\n",
        "das."
      ],
      "metadata": {
        "id": "SUlU-L5ey_MZ"
      },
      "id": "SUlU-L5ey_MZ"
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "_Egm6Cqryps9"
      },
      "id": "_Egm6Cqryps9",
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "source": [
        "##Estimadores\n",
        "\n",
        "Un estimador es una regla o función que se utiliza para calcular un valor aproximado de un parámetro poblacional desconocido, basándose en los datos de una muestra aleatoria extraída de esa población. El valor específico obtenido al aplicar esta regla a una muestra particular se denomina estimación."
      ],
      "metadata": {
        "id": "7KeP_JkeqWNo"
      },
      "id": "7KeP_JkeqWNo"
    },
    {
      "cell_type": "markdown",
      "source": [
        "Un estimador puntual para un parámetro desconocido θ es una estadística denotada por θ que se propone para estimar el parámetro.\n",
        "\n",
        "Propiedades más importantes de los estimadores:\n",
        "\n",
        "1. Insesgadez (Unbiasedness):\n",
        "\n",
        "Un estimador $\\hat{\\theta}$\n",
        "  de un parámetro θ es insesgado si su valor esperado (la media de su distribución muestral) es igual al verdadero valor del parámetro.\n",
        "Matemáticamente: $ E[\\hat{\\theta}]=\\theta$\n",
        "\n",
        "El sesgo se define como $\\text{Sesgo}(\\hat{\\theta}) = E[\\hat{\\theta}]-\\theta $\n",
        "\n",
        "2. Eficiencia (Efficiency):\n",
        "\n",
        "La eficiencia se refiere a la precisión de un estimador. Un estimador es más eficiente que otro si tiene una menor varianza (o error cuadrático medio) para el mismo tamaño de muestra.\n",
        "\n",
        "3. Consistencia (Consistency):\n",
        "Un estimador $\\hat{\\theta}_n$ basado en una muestra de tamaño n es consistente si converge al verdadero valor del parámetro θ a medida que el tamaño de la muestra n tiende a infinito.\n",
        "\n",
        "La consistencia asegura que, con una cantidad suficientemente grande de datos, nuestro estimador estará muy cerca del valor real del parámetro.\n",
        "Ejemplo: Bajo ciertas condiciones, la media muestral es un estimador consistente de la media poblacional (esto se relaciona con la Ley de los Grandes Números).\n",
        "\n",
        "\n",
        "4. Suficiencia (Sufficiency):\n",
        "\n",
        "Un estadístico es suficiente si contiene toda la información relevante de la muestra para estimar el parámetro de interés. Esto significa que, una vez que conocemos el valor del estadístico suficiente, cualquier otra información adicional de la muestra no proporciona más información sobre el parámetro.\n",
        "Formalmente, un estadístico T(X) es suficiente para un parámetro θ si la distribución condicional de la muestra X dado T(X) no depende de θ.\n",
        "Los estimadores basados en estadísticos suficientes tienden a ser buenos estimadores.\n",
        "\n",
        "5. Robustez (Robustness):\n",
        "\n",
        "Un estimador es robusto si su rendimiento no se ve afectado significativamente por pequeñas desviaciones de los supuestos del modelo estadístico (por ejemplo, la presencia de valores atípicos o ligeras violaciones de la normalidad).\n",
        "Los estimadores robustos son útiles en la práctica, ya que los datos reales a menudo no cumplen perfectamente los supuestos teóricos."
      ],
      "metadata": {
        "id": "-Y_flvVlqhGw"
      },
      "id": "-Y_flvVlqhGw"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "f6fac274-4997-46e0-8bac-8c276a8a2671"
      },
      "source": [
        "# Intervalos de Confianza"
      ],
      "id": "f6fac274-4997-46e0-8bac-8c276a8a2671"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "02db30e8-0f1b-4960-bb22-d24bc200e8e8"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import scipy.stats as st"
      ],
      "id": "02db30e8-0f1b-4960-bb22-d24bc200e8e8"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "83757f12-3911-4534-b161-7ab242dfac79"
      },
      "source": [
        "## Intervalo de Confianza para la media de una distribución normal (σ conocida)\n",
        "\n",
        "Sea $X_1, \\dots, X_n$ una m.a. $X_i \\sim \\mathcal{N}(\\mu, \\sigma^2)$. Entonces:\n",
        "\n",
        "- $\\bar{X} \\sim \\mathcal{N}(\\mu, \\frac{\\sigma^2}{n})$\n",
        "- $Z = \\frac{\\bar{X} - \\mu}{\\sigma / \\sqrt{n}} \\sim \\mathcal{N}(0,1)$\n",
        "\n",
        "### Nivel de significancia (error): $\\alpha$\n",
        "\n",
        "El intervalo de confianza se basa en que:\n",
        "$$\n",
        "\\mathbb{P}\\left( -z_{\\alpha/2} < \\frac{\\bar{X} - \\mu}{\\sigma / \\sqrt{n}} < z_{\\alpha/2} \\right)\n",
        "= \\mathbb{P}\\left( \\bar{X} - z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}} < \\mu < \\bar{X} + z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}} \\right)\n",
        "= 1 - \\alpha\n",
        "$$\n",
        "\n",
        "### El intervalo del $(1 - \\alpha) \\cdot 100\\%$ de confianza para $\\mu$ (con $\\sigma$ conocida) es:\n",
        "\n",
        "$$\n",
        "\\left( \\bar{X} - z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}}, \\quad \\bar{X} + z_{\\alpha/2} \\frac{\\sigma}{\\sqrt{n}} \\right)\n",
        "$$\n",
        "donde\n",
        "\n",
        "- $\\sigma$ = desviación estándar  \n",
        "- $\\frac{\\sigma}{\\sqrt{n}}$ = error estándar de la media  \n",
        "- $z_{\\alpha/2}$ determina el nivel de confianza  \n",
        "- El intervalo está centrado en $\\bar{X}$\n",
        "\n",
        "**Observación**\n",
        "\n",
        "- A mayor $n$, menor es el error estándar, y el intervalo de confianza es más pequeño.\n",
        "- Esto hace que se acerque más a la media $\\mu$, es decir, que haya menor variación.\n"
      ],
      "id": "83757f12-3911-4534-b161-7ab242dfac79"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4167e3ab-019c-469a-8ec8-3dd4fb04fb3a"
      },
      "source": [
        "**Ejemplo 1** Para tratar de estimar la media de consumo por cliente en un gran restaurante, se reunieron datos de una muestra de 49 clientes durante 3 semanas.\n",
        "\n",
        "**a)** Supongamos que la **desviación estándar de la población** es de $\\$2.50$. ¿Cuál es el error estándar de la media?\n",
        "\n",
        "**b)** Con un nivel de confianza del $95\\%$, ¿cuál es el margen de error?\n",
        "\n",
        "**c)** Si la **media de la muestra** es de $\\$22.60$, cuál es el intervalo de confianza del $95\\%$ para la media de la población?"
      ],
      "id": "4167e3ab-019c-469a-8ec8-3dd4fb04fb3a"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "8fab1175-2fdd-46cf-b5e9-afa96fd58bd8",
        "outputId": "ce23d383-bc47-45b0-f43e-476d4308ea66"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            " a) Error estándar de la media: 0.36\n",
            " b) Margen de error con 95% de confianza: 0.70\n",
            " c) Intervalo de confianza del 95%: (21.90,23.30)\n"
          ]
        }
      ],
      "source": [
        "# Datos\n",
        "n=49\n",
        "sigma = 2.50\n",
        "media_muestral = 22.60\n",
        "confianza = 0.95\n",
        "\n",
        "# a) Error estándar de la media\n",
        "error_estandar = sigma / np.sqrt(n)\n",
        "#error_estandar\n",
        "print(f\" a) Error estándar de la media: {error_estandar:.2f}\")\n",
        "\n",
        "# b) Margen de error\n",
        "z = st.norm.ppf(1-(1-confianza) / 2)\n",
        "margen_error = z * error_estandar\n",
        "#margen_error\n",
        "print(f\" b) Margen de error con 95% de confianza: {margen_error:.2f}\")\n",
        "\n",
        "# c)\n",
        "limite_inferior = media_muestral - margen_error\n",
        "limite_superior = media_muestral + margen_error\n",
        "print(f\" c) Intervalo de confianza del 95%: ({limite_inferior:.2f},{limite_superior:.2f})\")"
      ],
      "id": "8fab1175-2fdd-46cf-b5e9-afa96fd58bd8"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "355a09d1-ea4b-4bca-8687-634b9a711160"
      },
      "source": [
        "$1-\\alpha=.95$, implica que $z_{\\alpha/2} = z_{0.025} = 1.96$"
      ],
      "id": "355a09d1-ea4b-4bca-8687-634b9a711160"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "84d9699b-83a4-41ee-ab46-971262070bde"
      },
      "source": [
        "**Ejemplo 2** Supongamos que se toma una muestra aleatoria de 100 personas para estimar la media del peso de una población, y se obtiene que la media muestral es de $70$ kg con una desviación estándar que es conocida de $10$ kg. Para un nivel de confianza del $95\\%$, calcular el intervalo de confianza"
      ],
      "id": "84d9699b-83a4-41ee-ab46-971262070bde"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "bc091cc7-4fc7-4d23-ae93-9c058c82d073",
        "outputId": "b43b8dfb-f64e-4eae-bf50-0296e7de0c90"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Intervalo de confianza del 95% es: (68.04003601545995, 71.95996398454005)\n"
          ]
        }
      ],
      "source": [
        "# Datos\n",
        "n = 100\n",
        "media_muestral = 70\n",
        "sigma = 10\n",
        "nivel_confianza = 0.95\n",
        "error_estandar = sigma / np.sqrt(n)\n",
        "\n",
        "#Utilizaremos la función scipy.stats.norm.interval\n",
        "# Sintaxis\n",
        "# scipy.stats.norm.interval(confidence, loc = media, scale = error_estandar )\n",
        "\n",
        "intervalo = st.norm.interval(confidence = nivel_confianza, loc = media_muestral, scale = error_estandar)\n",
        "print(f\"Intervalo de confianza del 95% es: {intervalo}\")\n"
      ],
      "id": "bc091cc7-4fc7-4d23-ae93-9c058c82d073"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "cb7790f8-3bb4-4e42-b70b-92c2897699a3",
        "outputId": "2ba1b952-f8d7-42a1-bb47-68b2e3dd1ce1"
      },
      "outputs": [
        {
          "data": {
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",
            "text/plain": [
              "<Figure size 1000x500 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "# Puntos para graficar la curva normal\n",
        "x = np.linspace(media_muestral - 4*error_estandar, media_muestral + 4*error_estandar, 500)\n",
        "y = st.norm.pdf(x, loc=media_muestral, scale=error_estandar)\n",
        "\n",
        "# Gráfica\n",
        "plt.figure(figsize=(10, 5))\n",
        "plt.plot(x, y, label='Distribución normal', color='black')\n",
        "\n",
        "# Sombrear el intervalo de confianza\n",
        "plt.fill_between(x, y, where=(x >= intervalo[0]) & (x <= intervalo[1]), color='skyblue', alpha=0.6, label='IC 95%')\n",
        "\n",
        "# Líneas verticales\n",
        "plt.axvline(intervalo[0], color='blue', linestyle='--', label=f'IC inferior = {intervalo[0]:.2f}')\n",
        "plt.axvline(intervalo[1], color='blue', linestyle='--', label=f'IC superior = {intervalo[1]:.2f}')\n",
        "plt.axvline(media_muestral, color='red', linestyle='-', label=f'Media muestral = {media_muestral}')\n",
        "\n",
        "plt.title('Intervalo de confianza del 95% para la media ($\\\\sigma$ conocida)', fontsize=14)\n",
        "plt.xlabel('Valor de la variable')\n",
        "plt.ylabel('Densidad')\n",
        "plt.legend()\n",
        "plt.grid(True)\n",
        "plt.show()"
      ],
      "id": "cb7790f8-3bb4-4e42-b70b-92c2897699a3"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5d7ff38c-23bf-47af-83ce-74186a9c4885"
      },
      "source": [
        "## Intervalo de Confianza para la media $\\mu$ de una distribución normal ($\\sigma$ deconocida)\n",
        "\n",
        "Sea $X_1, \\dots, X_n$ una m.a. $X_i \\sim \\mathcal{N}(\\mu, \\sigma^2)$. Entonces:\n",
        "\n",
        "- $\\bar{X} \\sim \\mathcal{N}(\\mu, \\frac{\\sigma^2}{n})$\n",
        "- $Z = \\frac{\\bar{X} - \\mu}{\\sigma / \\sqrt{n}} \\sim \\mathcal{N}(0,1)$\n",
        "\n",
        "Si el tamaño de la muestra es menor a 30, se utiliza la $t$:\n",
        "### Estadístico t\n",
        "\n",
        "Definimos el estadístico $t$ de la siguiente manera:\n",
        "$$T = \\frac{\\bar{X}-\\mu}{s/\\sqrt{n}} \\sim t_{(n-1)} $$\n",
        "\n",
        "### El intervalo del $(1 - \\alpha) \\cdot 100\\%$ de confianza para $\\mu$ (con $\\sigma$ desconocida) es:\n",
        "\n",
        "$$\n",
        "\\left( \\bar{X} - t_{\\alpha/2} \\frac{s}{\\sqrt{n}}, \\quad \\bar{X} + t_{\\alpha/2} \\frac{s}{\\sqrt{n}} \\right)\n",
        "$$\n",
        "donde\n",
        "\n",
        "- $s$ = desviación estándar muestral\n",
        "- $\\frac{s}{\\sqrt{n}}$ = error estándar de la media  \n",
        "- $t_{\\alpha/2}$ determina el nivel de confianza  \n",
        "- El intervalo está centrado en $\\bar{X}$"
      ],
      "id": "5d7ff38c-23bf-47af-83ce-74186a9c4885"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "53098df6-c305-4816-8917-a379c4dbb64b"
      },
      "source": [
        "**Ejemplo 3** Supongamos que tenemos los siguientes datos\n",
        "$$ datos = [45, 55, 67, 45, 68, 79, 98, 87, 84, 82] $$\n",
        "Calcular un intervalo de confianza para la media."
      ],
      "id": "53098df6-c305-4816-8917-a379c4dbb64b"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "f411d521-67c2-4cf4-a61c-1283ee39f5dc",
        "outputId": "4b5ecf4a-8373-4ff8-a166-fc63a9ab473a"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Media muestral: 71.00\n",
            "Error estandar: 5.75\n",
            "El intervalo de confianza del 95% es: (58.000521742293884, 83.99947825770612)\n"
          ]
        }
      ],
      "source": [
        "# Datos del ejemplo\n",
        "data = [45, 55, 67, 45, 68, 79, 98, 87, 84, 82]\n",
        "confidence = 0.95\n",
        "gl = len(data) - 1 # grados de liber\n",
        "\n",
        "# Media y error estandar\n",
        "mean = np.mean(data)\n",
        "error_est = st.sem(data)\n",
        "\n",
        "# Intervalo de confianza usando t de Student\n",
        "intervalo = st.t.interval(confidence, gl, loc = mean, scale = error_est)\n",
        "\n",
        "print(f\"Media muestral: {mean:.2f}\")\n",
        "print(f\"Error estandar: {error_est:.2f}\")\n",
        "print(f\"El intervalo de confianza del 95% es: {intervalo}\")\n"
      ],
      "id": "f411d521-67c2-4cf4-a61c-1283ee39f5dc"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "62e514a4-e078-4161-9f67-7623da916d34"
      },
      "source": [
        "**Ejemplo 4** Los artículos de cerámica utilizados sobre velas electricas sobrecargadas se rompen con diferentes presiones. Supongamos que los datos provienen de una distribución normal.\n",
        "\n",
        "La resistencia a la ruptura fue medida en una muestra de 100 artículos, y el promedio fue de $1750$ con un desviación estándar de 315.8\n",
        "\n",
        "**a)** Estimar con un nivel del confianza del $90\\%$ a la media poblacional de la presión de la ruptura.\n",
        "\n",
        "**b)** Estimar con un nivel del confianza del $90\\%$ a la varianza poblacional."
      ],
      "id": "62e514a4-e078-4161-9f67-7623da916d34"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "c1f0631a-ec18-4f2a-99d2-5da5c180ef34",
        "outputId": "c3dac233-e743-4580-b1f7-09837f3942d9"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "El intervalo de confianza del 90% es: (1698.0555224608725, 1801.9444775391275)\n",
            "El intervalo de confianza del 90% es: (80123.48643850331, 128146.71537457063)\n",
            "El intervalo de confianza del 90% es: (80123.48643850331, 128146.71537457063)\n"
          ]
        }
      ],
      "source": [
        "from scipy.stats import chi2\n",
        "# datos\n",
        "n = 100\n",
        "media_muestral = 1750\n",
        "desv_estandar_muestral = 315.8\n",
        "confianza = 0.90\n",
        "\n",
        "# a) Usar la normal ya que el tamaño de la muestra es grande\n",
        "error_est = desv_estandar_muestral / np.sqrt(n)\n",
        "error_est\n",
        "intervalo_media = st.norm.interval(confidence=confianza, loc = media_muestral, scale = error_est)\n",
        "print(f\"El intervalo de confianza del 90% es: {intervalo_media}\")\n",
        "\n",
        "# b) Intervalo de confianza para la varianza (usar chi-cuadrada)\n",
        "alpha = 1-confianza\n",
        "gl = n-1\n",
        "s2 = desv_estandar_muestral**2\n",
        "\n",
        "#Cuantiles de la chi-cuadrada\n",
        "chi2_inf = st.chi2.ppf(alpha / 2,df=gl)\n",
        "chi2_sup = st.chi2.ppf(1- alpha / 2,df=gl)\n",
        "\n",
        "# Intervalo de confianza\n",
        "intervalo_varianza = ((gl * s2) / chi2_sup, (gl * s2) / chi2_inf )\n",
        "print(f\"El intervalo de confianza del 90% es: {intervalo_varianza}\")\n",
        "\n",
        "#Otra forma\n",
        "chi2_low, chi2_high = chi2.interval(confianza,df=gl)\n",
        "intervalo_varianza1 = ((gl * s2) / chi2_high, (gl * s2) / chi2_low )\n",
        "print(f\"El intervalo de confianza del 90% es: {intervalo_varianza1}\")\n"
      ],
      "id": "c1f0631a-ec18-4f2a-99d2-5da5c180ef34"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "83178f8c-3f3f-4d0e-9a18-b46884bb5a4c"
      },
      "source": [
        "**Ejemplo**  El artículo *\"Evaluation of a Ventilation Strategy to Prevent Barotrauma in Patients at High Risk for Acute Respiratory Distress Syndrome\"* reportó sobre un experimento con 120 pacientes con anestesistas en cuidados intensivos (UCI), los cuales fueron divididos al azar en dos grupos, donde cada uno esta compuesto por 60 pacientes.\n",
        "\n",
        "- Grupo A: promedio de permanencia = 14.1 horas\n",
        "- Grupo B: promedio de permanencia = 17.5 horas\n",
        "- Desviación estándar en ambos = 5.1 hrs\n",
        "\n",
        "Encontrar un intervalo del $95\\%$ de confianza para la diferecia de medias poblacionales: $(\\mu_A - \\mu_B)$  "
      ],
      "id": "83178f8c-3f3f-4d0e-9a18-b46884bb5a4c"
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "4f710ffd-16aa-4205-b47a-c3f2c6a95648",
        "outputId": "64f32f7b-f82b-4b74-fc93-cd2b2e3fee4e"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Diferencia de las medias: -3.40\n",
            "Intervalo de confianza del 95%: (-5.22,-1.58)\n"
          ]
        }
      ],
      "source": [
        "#Datos\n",
        "n1 = 60\n",
        "n2 = 60\n",
        "media1 = 14.1\n",
        "media2 = 17.5\n",
        "sigma = 5.1\n",
        "confianza = 0.95\n",
        "alpha = 1-confianza\n",
        "#gl = n1 + n2 -2\n",
        "\n",
        "#valor critico\n",
        "z = st.norm.ppf(1 - alpha / 2)\n",
        "\n",
        "#Error estandar\n",
        "error_est = sigma * np.sqrt(1/n1 + 1/n2)\n",
        "dif_medias = media1 - media2\n",
        "margen_error = z *error_est\n",
        "\n",
        "lim_inf = dif_medias - margen_error\n",
        "lim_sup = dif_medias + margen_error\n",
        "print(f\"Diferencia de las medias: {dif_medias:.2f}\")\n",
        "print(f\"Intervalo de confianza del 95%: ({lim_inf:.2f},{lim_sup:.2f})\")"
      ],
      "id": "4f710ffd-16aa-4205-b47a-c3f2c6a95648"
    }
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