diff --git a/.gitignore b/.gitignore index 03fc1690..8d193625 100644 --- a/.gitignore +++ b/.gitignore @@ -1,4 +1,2 @@ - - -# Checkpoints will not be pushed. -.ipynb_checkpoints +.venv +.env diff --git a/notebook/problems.es.ipynb b/notebook/problems.es.ipynb index bbf9ad43..202878bf 100644 --- a/notebook/problems.es.ipynb +++ b/notebook/problems.es.ipynb @@ -1 +1,430 @@ -{"cells":[{"cell_type":"markdown","id":"b967ebc8","metadata":{},"source":["# Problemas de distribución de probabilidad"]},{"cell_type":"markdown","id":"c9b71587","metadata":{},"source":["## Distribución binomial\n","\n","En teoría de la probabilidad y estadística, la distribución binomial es la distribución de probabilidad discreta que da sólo dos resultados posibles en un experimento; por ejemplo, al lanzar una moneda, puede salir cara o cruz."]},{"cell_type":"code","execution_count":1,"id":"4eb16d6e","metadata":{},"outputs":[],"source":["from scipy.stats import binom\n","\n","# Definir todas las funciones de probabilidad relacionadas con esta distribución.\n","\n","def dbinom(x, size, prob = 0.5):\n"," \"\"\"\n"," Calcula la estimación puntual de la distribución binomial.\n"," \"\"\"\n"," result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def pbinom(q, size, prob = 0.5):\n"," \"\"\"\n"," Calcula el acumulado de la distribución binomial.\n"," \"\"\"\n"," result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def qbinom(p, size, prob = 0.5):\n"," \"\"\"\n"," Calcula la función cuantil a partir de la distribución binomial.\n"," \"\"\"\n"," result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n","\n"," return result\n","\n","def rbinom(n, size, prob = 0.5):\n"," \"\"\"\n"," Genera variables aleatorias a partir de la distribución binomial.\n"," \"\"\"\n"," result = binom.rvs(n = size, p = prob, size = n)\n","\n"," return result"]},{"cell_type":"code","execution_count":null,"id":"6cf6313a","metadata":{},"outputs":[],"source":["# Distribución binomial(10, 0.2), dónde n = 10 es el número de ensayos y p = 0.2 es la probabilidad de éxito en un solo ensayo\n","import numpy as np\n","\n","np.random.seed(42)\n","\n","print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n","print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n","print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")"]},{"cell_type":"code","execution_count":3,"id":"69fd07da","metadata":{},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{},"output_type":"display_data"}],"source":["import matplotlib.pyplot as plt\n","\n","np.random.seed(42)\n","\n","size = 10\n","prob = 0.2\n","data = rbinom(2000, size = 10, prob = 0.2)\n","\n","pmf = dbinom(data, size = size, prob = prob)\n","cdf = pbinom(data, size = size, prob = prob)\n","ppf = qbinom(data, size = size, prob = prob)\n","\n","fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n","\n","axis[0].stem(data, pmf, \"r-\")\n","axis[1].stem(data, cdf, \"b-\")\n","axis[2].stem(data, ppf, \"g-\")\n","\n","# Adjust the layout\n","plt.tight_layout()\n","\n","# Show the plot\n","plt.show()"]},{"cell_type":"markdown","id":"8aa7eaa0","metadata":{},"source":["## Ejercicio 1\n","\n","Escriba las funciones anteriores pero para distribuciones normales y uniformes."]},{"cell_type":"code","execution_count":4,"id":"98d5f012","metadata":{},"outputs":[],"source":["# TODO"]}],"metadata":{"interpreter":{"hash":"0f2f6c680cf484319d387fabac80ca4ff4fc33965036e02100b3fe02600f1423"},"kernelspec":{"display_name":"Python 3.10.1 64-bit","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.12.1"}},"nbformat":4,"nbformat_minor":5} \ No newline at end of file +{ + "cells": [ + { + "cell_type": "markdown", + "id": "b967ebc8", + "metadata": {}, + "source": [ + "# Problemas de distribución de probabilidad" + ] + }, + { + "cell_type": "markdown", + "id": "c9b71587", + "metadata": {}, + "source": [ + "## Distribución binomial\n", + "\n", + "En teoría de la probabilidad y estadística, la distribución binomial es la distribución de probabilidad discreta que da sólo dos resultados posibles en un experimento; por ejemplo, al lanzar una moneda, puede salir cara o cruz." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "4eb16d6e", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import binom\n", + "\n", + "# Definir todas las funciones de probabilidad relacionadas con esta distribución.\n", + "\n", + "def dbinom(x, size, prob = 0.5):\n", + " \"\"\"\n", + " Calcula la estimación puntual de la distribución binomial.\n", + " \"\"\"\n", + " result = binom.pmf(k = x, n = size, p = prob, loc = 0)\n", + "\n", + " return result\n", + "\n", + "def pbinom(q, size, prob = 0.5):\n", + " \"\"\"\n", + " Calcula el acumulado de la distribución binomial.\n", + " \"\"\"\n", + " result = binom.cdf(k = q, n = size, p = prob, loc = 0)\n", + "\n", + " return result\n", + "\n", + "def qbinom(p, size, prob = 0.5):\n", + " \"\"\"\n", + " Calcula la función cuantil a partir de la distribución binomial.\n", + " \"\"\"\n", + " result = binom.ppf(q = p, n = size, p = prob, loc = 0)\n", + "\n", + " return result\n", + "\n", + "def rbinom(n, size, prob = 0.5):\n", + " \"\"\"\n", + " Genera variables aleatorias a partir de la distribución binomial.\n", + " \"\"\"\n", + " result = binom.rvs(n = size, p = prob, size = n)\n", + "\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "6cf6313a", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probability that a Binomial(10, 0.2) takes the value 2: 0.30198988800000004\n", + "Probability that a Binomial(10, 0.2) will take a value less than 2: 0.6777995263999999\n", + "Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? 4.0\n", + "Generate 2000 random values from a Binomial(10, 0.2) distribution: [1 4 3 ... 0 0 1]\n" + ] + } + ], + "source": [ + "# Distribución binomial(10, 0.2), dónde n = 10 es el número de ensayos y p = 0.2 es la probabilidad de éxito en un solo ensayo\n", + "import numpy as np\n", + "\n", + "np.random.seed(42)\n", + "\n", + "print(f\"Probability that a Binomial(10, 0.2) takes the value 2: {dbinom(2, size = 10, prob = 0.2)}\")\n", + "print(f\"Probability that a Binomial(10, 0.2) will take a value less than 2: {pbinom(2, size = 10, prob = 0.2)}\")\n", + "print(f\"Which value of a Binomial(10, 0.2) has a cumulative probability of 0.9? {qbinom(0.9, size = 10, prob = 0.2)}\")\n", + "print(f\"Generate 2000 random values from a Binomial(10, 0.2) distribution: {rbinom(2000, size = 10, prob = 0.2)}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "69fd07da", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "\n", + "np.random.seed(42)\n", + "\n", + "size = 10\n", + "prob = 0.2\n", + "data = rbinom(2000, size = 10, prob = 0.2)\n", + "\n", + "pmf = dbinom(data, size = size, prob = prob)\n", + "cdf = pbinom(data, size = size, prob = prob)\n", + "ppf = qbinom(data, size = size, prob = prob)\n", + "\n", + "fig, axis = plt.subplots(3, 1, figsize = (5, 7))\n", + "\n", + "axis[0].stem(data, pmf, \"r-\")\n", + "axis[1].stem(data, cdf, \"b-\")\n", + "axis[2].stem(data, ppf, \"g-\")\n", + "\n", + "# Adjust the layout\n", + "plt.tight_layout()\n", + "\n", + "# Show the plot\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "8aa7eaa0", + "metadata": {}, + "source": [ + "## Ejercicio 1\n", + "Escriba las funciones anteriores pero para distribuciones normales y uniformes.\n" + ] + }, + { + "cell_type": "markdown", + "id": "33dd3eaf", + "metadata": {}, + "source": [ + "### Distribuciones normales" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "98d5f012", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import norm\n", + "\n", + "def dnorm(x, mean=0, std=1):\n", + " \"\"\"\n", + " Calcula la función de densidad de probabilidad (PDF) de la distribución normal.\n", + " \"\"\"\n", + " result = norm.pdf(x, loc=mean, scale=std)\n", + " return result\n", + "\n", + "def pnorm(q, mean=0, std=1):\n", + " \"\"\"\n", + " Calcula la función de distribución acumulativa (CDF) de la distribución normal.\n", + " \"\"\"\n", + " result = norm.cdf(q, loc=mean, scale=std)\n", + " return result\n", + "\n", + "def qnorm(p, mean=0, std=1):\n", + " \"\"\"\n", + " Calcula la función cuantil (inversa de la CDF) de la distribución normal.\n", + " \"\"\"\n", + " result = norm.ppf(p, loc=mean, scale=std)\n", + " return result\n", + "\n", + "def rnorm(n, mean=0, std=1):\n", + " \"\"\"\n", + " Genera variables aleatorias a partir de la distribución normal.\n", + " \"\"\"\n", + " result = norm.rvs(loc=mean, scale=std, size=n)\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "id": "cbb3cd6f", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Probabilidad de densidad en x = 0.5: 0.3520653267642995\n", + "Probabilidad de que X <= 1: 0.8413447460685429\n", + "Value of x such that P(X <= x) = 0.9: 1.2815515655446004\n", + "Generar 2000 valores aleatorios desde la Normal(0, 1) distribucion: [ 0.49671415 -0.1382643 0.64768854 ... -0.88187465 -0.16306696\n", + " -0.74490264]\n" + ] + } + ], + "source": [ + "np.random.seed(42)\n", + "\n", + "mean = 0 # Media\n", + "std = 1 # Desviación estándar\n", + "\n", + "print(f\"Probabilidad de densidad en x = 0.5: {dnorm(0.5, mean=mean, std=std)}\")\n", + "\n", + "print(f\"Probabilidad de que X <= 1: {pnorm(1, mean=mean, std=std)}\")\n", + "\n", + "print(f\"Value of x such that P(X <= x) = 0.9: {qnorm(0.9, mean=mean, std=std)}\")\n", + "\n", + "random_values = rnorm(2000, mean=mean, std=std)\n", + "print(f\"Generar 2000 valores aleatorios desde la Normal({mean}, {std}) distribucion: {random_values}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "id": "72205def", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(42)\n", + "\n", + "mean = 0 # Media\n", + "std = 1 # Desviación estándar\n", + "\n", + "# Generar 2000 valores aleatorios a partir de una distribución normal\n", + "data = rnorm(2000, mean=mean, std=std)\n", + "\n", + "# Calcular la PDF, CDF y PPF para los datos generados\n", + "pdf = dnorm(data, mean=mean, std=std)\n", + "cdf = pnorm(data, mean=mean, std=std)\n", + "ppf = qnorm(np.linspace(0.01, 0.99, len(data)), mean=mean, std=std) # Usamos valores entre 0.01 y 0.99 para evitar infinitos\n", + "\n", + "fig, axis = plt.subplots(3, 1, figsize=(5, 7))\n", + "\n", + "# Graficar PDF\n", + "axis[0].stem(data, pdf, \"r-\", markerfmt=\"ro\", linefmt=\"r-\", basefmt=\" \")\n", + "axis[0].set_title(\"PDF (Función de Densidad de Probabilidad)\")\n", + "axis[0].set_ylabel(\"Densidad\")\n", + "\n", + "# Graficar CDF\n", + "axis[1].stem(data, cdf, \"b-\", markerfmt=\"bo\", linefmt=\"b-\", basefmt=\" \")\n", + "axis[1].set_title(\"CDF (Función de Distribución Acumulativa)\")\n", + "axis[1].set_ylabel(\"Probabilidad Acumulada\")\n", + "\n", + "# Grafica PPF\n", + "axis[2].stem(np.linspace(0.01, 0.99, len(data)), ppf, \"g-\", markerfmt=\"go\", linefmt=\"g-\", basefmt=\" \")\n", + "axis[2].set_title(\"PPF (Función Cuantil)\")\n", + "axis[2].set_xlabel(\"Probabilidad Acumulada\")\n", + "axis[2].set_ylabel(\"Valores\")\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "id": "f3c4a61a", + "metadata": {}, + "source": [ + "### Distribuciones uniformes" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "id": "7b6183e6", + "metadata": {}, + "outputs": [], + "source": [ + "from scipy.stats import uniform\n", + "\n", + "def dunif(x, low=0, high=1):\n", + " \"\"\"\n", + " Calcula la función de densidad de probabilidad (PDF) de la distribución uniforme.\n", + " \"\"\"\n", + " result = uniform.pdf(x, loc=low, scale=high-low)\n", + " return result\n", + "\n", + "def punif(q, low=0, high=1):\n", + " \"\"\"\n", + " Calcula la función de distribución acumulativa (CDF) de la distribución uniforme.\n", + " \"\"\"\n", + " result = uniform.cdf(q, loc=low, scale=high-low)\n", + " return result\n", + "\n", + "def qunif(p, low=0, high=1):\n", + " \"\"\"\n", + " Calcula la función cuantil (inversa de la CDF) de la distribución uniforme.\n", + " \"\"\"\n", + " result = uniform.ppf(p, loc=low, scale=high-low)\n", + " return result\n", + "\n", + "def runif(n, low=0, high=1):\n", + " \"\"\"\n", + " Genera variables aleatorias a partir de la distribución uniforme.\n", + " \"\"\"\n", + " result = uniform.rvs(loc=low, scale=high-low, size=n)\n", + " return result" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "id": "a63dffc7", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "ProbabilidaD de densidad en x = 0.5: 1.0\n", + "Probabilidad de queX <= 0.7: 0.7\n", + "Value of x such that P(X <= x) = 0.9: 0.9\n", + "Generar 2000 valores aleatorios desde una distribucion uniformr(0, 1) distribution: [0.37454012 0.95071431 0.73199394 0.59865848 0.15601864 0.15599452\n", + " 0.05808361 0.86617615 0.60111501 0.70807258]\n" + ] + } + ], + "source": [ + "np.random.seed(42)\n", + "\n", + "low = 0 # Límite inferior\n", + "high = 1 # Límite superior\n", + "\n", + "print(f\"ProbabilidaD de densidad en x = 0.5: {dunif(0.5, low=low, high=high)}\")\n", + "\n", + "print(f\"Probabilidad de queX <= 0.7: {punif(0.7, low=low, high=high)}\")\n", + "\n", + "print(f\"Value of x such that P(X <= x) = 0.9: {qunif(0.9, low=low, high=high)}\")\n", + "\n", + "random_values = runif(2000, low=low, high=high)\n", + "print(f\"Generar 2000 valores aleatorios desde una distribucion uniformr({low}, {high}) distribution: {random_values[:10]}\") # Mostrar solo los primeros 10 valores" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "id": "60e10687", + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "# Generar datos aleatorios\n", + "data = runif(2000, low=low, high=high)\n", + "\n", + "# Calcular la PDF, CDF y PPF para los datos generados\n", + "pdf = dunif(data, low=low, high=high)\n", + "cdf = punif(data, low=low, high=high)\n", + "ppf = qunif(np.linspace(0.01, 0.99, len(data)), low=low, high=high) # Usamos valores entre 0.01 y 0.99 para evitar problemas en los extremos\n", + "\n", + "\n", + "fig, axis = plt.subplots(3, 1, figsize=(5, 7))\n", + "\n", + "# Graficar la PDF\n", + "axis[0].stem(data, pdf, \"r-\", markerfmt=\"ro\", linefmt=\"r-\", basefmt=\" \")\n", + "axis[0].set_title(\"PDF (Función de Densidad de Probabilidad)\")\n", + "axis[0].set_ylabel(\"Densidad\")\n", + "\n", + "# Graficar la CDF\n", + "axis[1].stem(data, cdf, \"b-\", markerfmt=\"bo\", linefmt=\"b-\", basefmt=\" \")\n", + "axis[1].set_title(\"CDF (Función de Distribución Acumulativa)\")\n", + "axis[1].set_ylabel(\"Probabilidad Acumulada\")\n", + "\n", + "# Graficar la PPF\n", + "axis[2].stem(np.linspace(0.01, 0.99, len(data)), ppf, \"g-\", markerfmt=\"go\", linefmt=\"g-\", basefmt=\" \")\n", + "axis[2].set_title(\"PPF (Función Cuantil)\")\n", + "axis[2].set_xlabel(\"Probabilidad Acumulada\")\n", + "axis[2].set_ylabel(\"Valores\")\n", + "\n", + "plt.tight_layout()\n", + "plt.show()" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.4" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +}