monte-carlo-simulation-of-rayleigh-distribution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulación Monte Carlo: Distribución de Rayleigh"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Descripción\n",
    "\n",
    "En este trabajo se estudia la duracción de un dispositivo constituido por $11$ componentes, que supondremos variables de *Rayleigh*, organizados en distintas configuraciones (serie, paralelo, stand-by, etc.). Para ello, utilizaremos el método de simulación *Monte Carlo*.\n",
    "\n",
    "El contenido de este trabajo se encuentra alojado en el siguiente repositorio: https://github.com/garciparedes/monte-carlo-simulation-rayleigh-distribution\n",
    "\n",
    "#### Contenidos\n",
    "\n",
    "  * [Introducción](#Introducción)\n",
    "  * [Apartado A - Simulación](#Apartado-A)\n",
    "    * [Apartado A.1 - Serie](#Apartado-A.1)\n",
    "    * [Apartado A.2 - Paralelo](#Apartado-A.2)\n",
    "    * [Apartado A.3 - Stand By](#Apartado-A.3)\n",
    "    * [Apartado A.4 - \"Al menos 6\"](#Apartado-A.4)\n",
    "    * [Apartado A.5 - Promedio](#Apartado-A.5)\n",
    "  * [Apartado B - Aproximaciones Puntuales](#Apartado-B)\n",
    "    * [Apartado B.1 - Serie](#Apartado-B.1)\n",
    "    * [Apartado B.2 - Paralelo](#Apartado-B.2)\n",
    "    * [Apartado B.3 - Stand By](#Apartado-B.3)\n",
    "    * [Apartado B.4 - \"Al menos 6\"](#Apartado-B.4)\n",
    "    * [Apartado B.5 - Promedio](#Apartado-B.5)\n",
    "  * [Apartado C - Estudio Analítico](#Apartado-C)\n",
    "    * [Apartado C.1 - Serie](#Apartado-C.1)\n",
    "    * [Apartado C.2 - Paralelo](#Apartado-C.2)\n",
    "  * [Conclusiones](#Conclusiones)\n",
    "\n",
    "\n",
    "#### Autor\n",
    "\n",
    "  * Sergio García Prado - [garciparedes.me](https://garciparedes.me)\n",
    "  \n",
    "\n",
    "#### Fecha\n",
    "\n",
    "  Mayo de 2018\n",
    "  \n",
    "\n",
    "#### Agradecimientos\n",
    "\n",
    "Me gustaría agradecer al profesor [Alfonso Gordaliza](http://www.eio.uva.es/infor/personas/alfonso.html) la revisión y correcciones sobre este trabajo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "rm(list = ls())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "library(ggplot2, warn.conflicts = FALSE)\n",
    "library(gridExtra, warn.conflicts = FALSE)\n",
    "library(tidyr, warn.conflicts = FALSE)\n",
    "library(dplyr, warn.conflicts = FALSE)\n",
    "library(magrittr, warn.conflicts = FALSE)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducción"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Unos determinados componentes de hardware informático tienen una vida útil que se comporta según la distribución de Rayleigh, de parámetro $\\sigma = 1$ año, según información fiable recibida del fabricante. La función de densidad del modelo de Rayleigh es sobradamente conocida por todos:* "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$f(x) = \\frac{x}{\\sigma^2}exp\\left(-\\frac{x^2}{2\\sigma^2}\\right), \\ x >0$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*Se tiene un equipo informático en cuya fabricación se incorpora un dispositivo formado **$11$ componentes** de los anteriores, que pueden estar acoplados según diferentes esquemas según se indica má adelante. Se supone que el equipo informático está funcionando ininterrumpidamente desde su puesta en marcha y que, idealmente, solo son posibles los fallos de los componetes que se están estudiando.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Uno de los primeros pasos antes de comenzar a realizar el ejercicio es el de definir la función de densidad de la distribución de Rayleigh, para poder trabajar con ella, así como estudiar su forma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.density <- function(x, sigma = 1) {\n",
    "    x / sigma ^ 2 * exp(- x ^ 2 / (2 * sigma ^ 2))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para la transformación cuantil, necesitaremos apoyarnos en la función de distribución de la variable aleatoria de estudio, la cual es fácil de obtener a partir de la función de densidad:"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\\begin{align}\n",
    "F(x) &= \\int_0^x f(t) \\,dt \\\\\n",
    "&= \\int_0^x \\frac{t}{\\sigma^2}exp\\left(-\\frac{t^2}{2\\sigma^2}\\right) \\,dt \\\\\n",
    "&= \\left(-exp\\left(-\\frac{t^2}{2\\sigma^2}\\right)\\right]_0^x \\\\\n",
    "&= 1 -exp\\left(-\\frac{x^2}{2\\sigma^2}\\right), \\ x >0\n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.distribution <- function(x, sigma = 1) {\n",
    "    1 - exp(- x ^ 2 / (2 * sigma ^ 2))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ahora, necesitamos invertir la función de distribución para poder utilizarla en la transformación cuantil, la cual utilizaremos para llevar a cabo la simulación Monte Carlo. A continuación se indican los pasos necesarios para la inversión de $F(x)$:\n",
    "\n",
    "\\begin{align}\n",
    "y  &= 1 -exp \\left( - \\frac{x^2}{2 \\sigma ^ 2}\\right) \\\\\n",
    "1 - y  &= exp \\left(- \\frac{x^2}{2 \\sigma ^ 2}\\right) \\\\\n",
    "ln\\left(1 - y \\right) &= -\\frac{x ^ 2}{2 \\sigma ^ 2} \\\\\n",
    "-2\\sigma^2ln\\left(1 - y \\right)  &= x^2 \\\\\n",
    "\\sigma\\sqrt{-2ln\\left(1 - y \\right)}  &= x \\\\\n",
    "\\end{align}\n",
    "\n",
    "Una vez invertida, la transformación cuantil para la distribución de Rayleigh es la siguiente:\n",
    "\n",
    "\\begin{equation}\n",
    "F^{-1}(x) = \\sigma\\sqrt{-2ln\\left(1 - x \\right)}, \\ x \\in [0, 1]\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.quantile <- function(x, sigma = 1) {\n",
    "    sigma * sqrt(- 2 * log(1 - x))\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para comprender mejor el comportamiento de esta distribución, es muy util representar gráficamente las funciones descritas superiormente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
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8qve+65R7AKAuZQol4hq1oCVyvF0OmtLtx00036vnrzzTc1X6ymgjmhqFPTRC/4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RuRG1wx7RjlHBESr8hUU6vJGzFR2MBoLY8MORQD8cgeBjGRIgAQsTiDuk4ChVil4m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\nAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 3, repr.plot.width = 9)\n",
    "grid.arrange(\n",
    "    ggplot(data.frame(x=c(0, 6)), aes(x)) + \n",
    "        stat_function(fun = rayleigh.density, col = \"red\") +\n",
    "        ylab(\"f(x)\") + \n",
    "        ggtitle(\"Función de Densidad\"), \n",
    "    ggplot(data.frame(x=c(0, 6)), aes(x)) + \n",
    "        stat_function(fun = rayleigh.distribution, col = \"red\") +\n",
    "        ylab(\"F(x)\") + \n",
    "        ggtitle(\"Función de Distribución\"), \n",
    "    ggplot(data.frame(x=c(0, 1)), aes(x)) + \n",
    "        stat_function(fun = rayleigh.quantile, col = \"red\") +\n",
    "        ylab(\"F^(-1)(x)\") + \n",
    "        ggtitle(\"Transformación Cuantil\"),\n",
    "    ncol = 3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Tal y como se puede apreciar en los gráficos, la Distribución de Rayleigh no es simétrica. Su forma recuerda a la de distribución de la $\\chi^2$ con una cola más pesada hacía la derecha. En nuestro caso, se ha fijado el parámetro de escala $\\sigma = 1$ por lo que la mayoría de masa de probabilidad se localiza en dicha zona del soporte. La función de distribución refleja lo que se ha indicado anteriormente, pero además deja ver claramente el nivel de asimetría de la variable. La transformación cuantil es la función inversa de la de densidad, por lo que \"refleja\" dicho comportamiento."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La distribución de *Rayleigh* surge como un caso particular de la distribución de *Weibull*, la cual permite modelizar un gran número de situaciones temporales. En concreto, la relación entre estas dos distribuciones es la siguiente:\n",
    "\n",
    "$$\n",
    "Rayleigh\\left(\\sigma\\right) \\equiv Weibull\\left(\\sqrt{2}\\sigma, 2\\right)\n",
    "$$\n",
    "\n",
    "Donde el primer parámetro de *Weibull* se refiere a la escala y el segundo a la forma."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apartado A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*Realizar un experimento de simulación Montecarlo para tener una aproximación razonable del comportamiento de las variables que se describen a continuación.*\n",
    "\n",
    "*En el trabajo hay que describir y justificar razonadamente todos los pasos que se dan en el experimento de simulación.\n",
    "Se recomienda recordar lo estudiado acerca de la transformación cuantil y la simulación de variables aleatorias en el Capítulo 4 del material de *del Barrio & Gordaliza*.*\n",
    "\n",
    "*Se recomienda simular entre $5000$ y $10000$ muestras y presentar sendos histogramas como aproximaciones empíricas al modelo probabilístico (función de densidad) de cada una de las variables indicadas en los cinco subapartados.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La simulación *Monte Carlo* se basa en la generación de valores de una determinada variable aleatoria con distribución seguida mediante la función inversa de la función de distribución y la generación aleatoria de valores de manera uniforme en el intervalo $[0, 1]$.\n",
    "\n",
    "La intuicción detrás de este procedimiento es la siguiente: Si \"elegimos\" al azar y de manera uniforme cuantiles de una determinada distribución $F$, entonces al final estaremos obteniendo realizaciones de dicha distribución.\n",
    "\n",
    "Esto, se puede llevar a cabo de manera automática si se generan números aleatorios de una distribución $U \\sim U(0, 1)$ y después se transforman mediante la función de distribución inversa (transformación cuantil) que se acaba de calcular. Entonces si aplicamos $X = F^{-1}(U)$ se puede demostrar desarrollando la función de densidad de la variable $X$, que habremos conseguido $X \\sim F$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Por tanto, esta será la intuicción que utilizaremos para realizar una simulación sobre variables de *Rayleigh*. En concreto, y siguiendo el enunciado propuesto diseñaremos el experimento de la siguiente manera:\n",
    "\n",
    "Sea: \n",
    "\n",
    "$$U_i = \\left(U_{i1}, ..., U_{ij}, ..., U_{i11}\\right) \\ v.a.i.i.d. \\ | \\ U_{ij} \\sim U\\left(0,1\\right) \\ \\forall i \\in \\{1, ..., 7500\\} $$\n",
    "\n",
    "Nuestras variables aleatorias (en este caso vector por referirse a 11 componentes) de partida, entonces realizaremos la transformación cuantil sobre todas ellas de tal manera que:\n",
    "\n",
    "\\begin{align}\n",
    "F^{-1}\\left(U_i\\right) &= \\left(F^{-1}\\left(U_{i1}\\right), ..., F^{-1}\\left(U_{ij}\\right), ..., F^{-1}\\left(U_{i11}\\right)\\right) \\\\\n",
    " &= \\left(X_{i1}, ..., X_{ij}, ..., X_{i11}\\right) \\\\\n",
    " &= X_i\n",
    "\\end{align}\n",
    "\n",
    "Por lo que habremos llegado a nuestra simulación de variables de *Rayleigh* mediante la transformación cuantil de variables de una distribución *Uniforme* en el intervalo $[0,1]$ tal y como se indica a continuación:\n",
    "\n",
    "$$X_i = \\left(X_{i1}, ..., X_{ij}, ..., X_{i11}\\right) \\ v.a.i.i.d. \\ | \\ X_{ij} \\sim F \\ \\forall i \\in \\{1, ..., 7500\\}$$\n",
    "\n",
    "Además, debido a la suposición de independencia entre variables, es posible generar todos los valores como una muestra aleatoria simple y después agruparlos en vectores de $11$ componentes. A continuación se incluye el código necesario para realizar dicha generación de variables con distribución *Uniforme* así como la tranformación cuantil:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "n.s <- 7500\n",
    "n.c <- 11\n",
    "x.limits <- c(0, 6)\n",
    "\n",
    "uniform.sample <- \n",
    "    matrix(runif(n.s * n.c, min = 0, max = 1), ncol = n.c, nrow = n.s) %>%\n",
    "    as.data.frame() %>%\n",
    "    set_colnames(sprintf(\"C%02d\", 1:n.c))\n",
    "\n",
    "rayleigh.sample <- \n",
    "    rayleigh.quantile(uniform.sample)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Los histogramas resultante de las variables con distribución $Uniforme$ sobre cada componente se puede visualizar a continuación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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y9yerX72J1vt27dVJruL975kcWmUFdf/QvZaLFU2iYtd5xERaU0liWk6267uYOK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NHJoEfwN/+BFpZgK2yidzCrmFPPLII7ld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\nAAEEEEAAAQQQQACBaAj8P0u8Ge1H7hPYAAAAAElFTkSuQmCC",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 5, repr.plot.width = 9)\n",
    "uniform.sample %>%\n",
    "    gather() %>% \n",
    "    ggplot(aes(value)) +\n",
    "        scale_x_continuous(limits = c(0, 1)) + \n",
    "        geom_histogram(aes(y = ..density..), binwidth = 0.05) +\n",
    "        stat_function(fun = dunif, col = \"red\") +\n",
    "        facet_wrap(~ key, scales = \"free\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Así como los histogramas de cada componente tras la realización de la transformación cuantil, resultando en simulaciones de la variables de $Rayleigh$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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IgRI6hr166Gd/XquV6yZAnJVnMyowuJ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JBMTAEUm5LWkVAkJACAgBISAEhIAQEAJCQAgIASEQpgTEwBGmGSvJEgJCQAgIASEg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\nwYaFHLuNVtVJC1qat7DX2G/16lB7Xib6ZC77IkJACPiPgHX3HrKtWEnFp3c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lHY28vDw1NQXxOurXr+9+2gn/33nnncd5cDRs2JCOHDly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8Sqo7yQlpZGxdypiVVFIEF2ZtmwYQP179+f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\nAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 5, repr.plot.width = 9)\n",
    "rayleigh.sample %>%\n",
    "    select(starts_with(\"C\")) %>%\n",
    "    gather() %>% \n",
    "    ggplot(aes(x = value)) +\n",
    "        scale_x_continuous(limits = x.limits) + \n",
    "        geom_histogram(aes(y = ..density..), binwidth = 0.1) +\n",
    "        stat_function(fun = rayleigh.density, col = \"red\") +\n",
    "        facet_wrap(~ key)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Una vez generada la simulación resultante, se procederá a resolver las distintas cuestiones sobre distintas suposiciones sobre la forma en que se conectan los componentes del dispositivo. Para ello, el procedimiento que se seguirá es el siguiente: Primero se justificará el procedimiento utilizado para posteriormente realizar la pertinente transformación de los datos, que se representará de manera gráfica."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado A.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*La duración del dispositivo si los componentes están acoplados **en serie** (el dispositivo funciona mientras todos los componentes estén en funcionamiento).*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como es obvio, diremos que la duracción de un dispositivo acoplado en serie es la del mínimo de los componentes que la componen. Por tanto, en cada observación de la muestra, seleccionaremos el mínimo de entre sus componentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.sample$series <- \n",
    "    rayleigh.sample %>% \n",
    "    dplyr::select(dplyr::starts_with(\"C\")) %>% \n",
    "    apply(1, min)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JGXnlAPAgQIECBAgAABAgQIECBAoGIB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\nRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 4, repr.plot.width = 9)\n",
    "rayleigh.sample %>%\n",
    "    ggplot(aes(series)) +\n",
    "    scale_x_continuous(limits = x.limits) + \n",
    "    geom_histogram(bins = 60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el [Apartado B.1](#Apartado-B.1) se calculan distintos estadísticos sobre la muestra generada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado A.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*La duración del dispositivo si los componentes están acoplados **en paralelo** (el dispositivo funciona mientras alguno de los componentes estén funcionamiento)*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como es obvio, diremos que la duracción de un dispositivo acoplado en paralelo es la del máximo de los componentes que la componen. Por tanto, en cada observación de la muestra, seleccionaremos el máximo de entre sus componentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.sample$parallel <- \n",
    "    rayleigh.sample %>% \n",
    "    dplyr::select(dplyr::starts_with(\"C\")) %>% \n",
    "    apply(1, max)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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qbCRdpeurzxjW+MX/7yl6Wrsie2pJEeRVpKR6gUKW6xFkcgjd5It3+1t7cXJ2iR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\nyJfA/wNqJ7Xo7o7zUgAAAABJRU5ErkJggg==",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 4, repr.plot.width = 9)\n",
    "rayleigh.sample %>%\n",
    "    ggplot(aes(parallel)) +\n",
    "    scale_x_continuous(limits = x.limits) + \n",
    "    geom_histogram(bins = 60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el [Apartado B.2](#Apartado-B.2) se calculan distintos estadísticos sobre la muestra generada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado A.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*La duración del dispositivo si los componentes están **acoplados en \"stand by\"**, según se explica para esta modalidad de acoplamiento en el material de *del Barrio & Gordaliza* en el capítulo \"Modelos de fiabilidad. La ley de Weibull.\"*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Como es obvio, diremos que la duracción de un dispositivo acoplado en \"stand by\" es la suma de las duraciones de cada componentes si entendemos que no puede funcionar ningún componente de manera simultanea y cuando uno de estos falla, comienza a funcionar otro de manera inmediata.Por tanto, en cada observación de la muestra, seleccionaremos la suma de sus componentes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.sample$stand.by <- \n",
    "    rayleigh.sample %>% \n",
    "    dplyr::select(dplyr::starts_with(\"C\")) %>% \n",
    "    apply(1, sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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BAgQIAAAQJ1IiDAUScdrZkECBAgQIAAAQIECBAgQKDMAgIcZe5dbSNAgAABAgQI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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 4, repr.plot.width = 9)\n",
    "rayleigh.sample %>%\n",
    "    ggplot(aes(stand.by)) +\n",
    "    scale_x_continuous(limits = x.limits * n.c / 2) + \n",
    "    geom_histogram(bins = 60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el [Apartado B.3](#Apartado-B.3) se calculan distintos estadísticos sobre la muestra generada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado A.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*La duración del dispositivo si los componentes están acoplados de tal forma que **el dispositivo funciona mientras al menos seis de los componentes estén en funcionamiento**.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para estudiar el fenómeno referido a que se mantengan funcionando de manera correcta al menos $6$ de los componentes, es equivalente a estudiar el estadístico ordenado situado en la sexta posición, es decir, $X_{(6)}$. Por tanto, en este caso se utilizará el tiempo de fallo del sexto componente para cada observación de la simulada."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.sample$least.6 <- \n",
    "    rayleigh.sample %>% \n",
    "    dplyr::select(dplyr::starts_with(\"C\")) %>% \n",
    "    apply(1, sort) %>%\n",
    "    {t(.)[, 6]}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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ECAAAECxRSQ4Chmu4maAAECBAgQIECA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",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 4, repr.plot.width = 9)\n",
    "rayleigh.sample %>%\n",
    "    ggplot(aes(least.6)) +\n",
    "    scale_x_continuous(limits = x.limits) + \n",
    "    geom_histogram(bins = 60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el [Apartado B.4](#Apartado-B.4) se calculan distintos estadísticos sobre la muestra generada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado A.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*La **duración promedio de los once componentes** si se supone que todos comienzan su funcionamiento a la vez y el dispositivo se mantiene activo hasta que todos han fallado.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se pide estudiar el promedio de la duración de cada componente. Por tanto, aplicaremos el promedio sobre cada observación de la muestra."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.sample$mean <- \n",
    "    rayleigh.sample %>% \n",
    "    dplyr::select(dplyr::starts_with(\"C\")) %>% \n",
    "    apply(1, mean)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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RAgQIAAAQIECBAgQIAAgVwEBBy59IQ6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\nSUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "options(repr.plot.height = 4, repr.plot.width = 9)\n",
    "rayleigh.sample %>%\n",
    "    ggplot(aes(mean)) +\n",
    "    scale_x_continuous(limits = x.limits) + \n",
    "    geom_histogram(bins = 60)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el [Apartado B.5](#Apartado-B.5) se calculan distintos estadísticos sobre la muestra generada."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apartado B"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*En todos los casos que se decriben en el apartado anterior, a partir de las simulaciones obtener una aproximación (estimación puntual) de los siguientes parámetros de la variable estudiaba: la media, la desviación típica, el percentil $2$ y la probabilidad de que la variable supere el valor $1.5$ añós.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el cálculo los parámetros, se va a construir una función que simplifique la implementación en *R*:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "ApproximateParameter <- function(x) {\n",
    "    list(\n",
    "        mean = mean(x),\n",
    "        sd = sd(x),\n",
    "        quantile.02 = quantile(x, 0.02, names = FALSE),\n",
    "        p.upper.1.5 = sum(x > 1.5) / length(x)\n",
    "    )\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado B.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se utilizarán los datos transformados en el [Apartado A.1](#Apartado-A.1), y referidos a *La duración del dispositivo si los componentes están acoplados **en serie** (el dispositivo funciona mientras todos los componentes estén en funcionamiento).*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$mean</dt>\n",
       "\t\t<dd>0.379743849192924</dd>\n",
       "\t<dt>$sd</dt>\n",
       "\t\t<dd>0.199021277761433</dd>\n",
       "\t<dt>$quantile.02</dt>\n",
       "\t\t<dd>0.0595719486436585</dd>\n",
       "\t<dt>$p.upper.1.5</dt>\n",
       "\t\t<dd>0</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$mean] 0.379743849192924\n",
       "\\item[\\$sd] 0.199021277761433\n",
       "\\item[\\$quantile.02] 0.0595719486436585\n",
       "\\item[\\$p.upper.1.5] 0\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$mean\n",
       ":   0.379743849192924\n",
       "$sd\n",
       ":   0.199021277761433\n",
       "$quantile.02\n",
       ":   0.0595719486436585\n",
       "$p.upper.1.5\n",
       ":   0\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$mean\n",
       "[1] 0.3797438\n",
       "\n",
       "$sd\n",
       "[1] 0.1990213\n",
       "\n",
       "$quantile.02\n",
       "[1] 0.05957195\n",
       "\n",
       "$p.upper.1.5\n",
       "[1] 0\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ApproximateParameter(rayleigh.sample$series)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estos valores son coherentes con el experimento que se pretende a estudiar, así como con la simulación realizada, estando la distribución muy próximos a  $0$ en el soporte, tanto que la probabilidad aproximada de que el dispositivo dure más de un año y medio se convierte en $0$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado B.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se utilizarán los datos transformados en el [Apartado A.2](#Apartado-A.2), y referidos a *La duración del dispositivo si los componentes están acoplados **en paralelo** (el dispositivo funciona mientras alguno de los componentes estén funcionamiento)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$mean</dt>\n",
       "\t\t<dd>2.41004122115448</dd>\n",
       "\t<dt>$sd</dt>\n",
       "\t\t<dd>0.488574929628598</dd>\n",
       "\t<dt>$quantile.02</dt>\n",
       "\t\t<dd>1.55413833435374</dd>\n",
       "\t<dt>$p.upper.1.5</dt>\n",
       "\t\t<dd>0.987466666666667</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$mean] 2.41004122115448\n",
       "\\item[\\$sd] 0.488574929628598\n",
       "\\item[\\$quantile.02] 1.55413833435374\n",
       "\\item[\\$p.upper.1.5] 0.987466666666667\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$mean\n",
       ":   2.41004122115448\n",
       "$sd\n",
       ":   0.488574929628598\n",
       "$quantile.02\n",
       ":   1.55413833435374\n",
       "$p.upper.1.5\n",
       ":   0.987466666666667\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$mean\n",
       "[1] 2.410041\n",
       "\n",
       "$sd\n",
       "[1] 0.4885749\n",
       "\n",
       "$quantile.02\n",
       "[1] 1.554138\n",
       "\n",
       "$p.upper.1.5\n",
       "[1] 0.9874667\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ApproximateParameter(rayleigh.sample$parallel)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el caso de la configuración en paralelo, la duración del dispositivo es mucho mayor, por ser necesario que todos los componentes fallen antes de que el dispositivo deje de funcionar. Además, en esta configuración la probabilidad de que el dispositivo dure más de un año y medio es alta."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado B.3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se utilizarán los datos transformados en el [Apartado A.3](#Apartado-A.3), y referidos a *La duración del dispositivo si los componentes están **acoplados en \"stand by\"**, según se explica para esta modalidad de acoplamiento en el material de *del Barrio & Gordaliza* en el capítulo \"Modelos de fiabilidad. La ley de Weibull.\"*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$mean</dt>\n",
       "\t\t<dd>13.8145687726395</dd>\n",
       "\t<dt>$sd</dt>\n",
       "\t\t<dd>2.16623011963433</dd>\n",
       "\t<dt>$quantile.02</dt>\n",
       "\t\t<dd>9.55368421000001</dd>\n",
       "\t<dt>$p.upper.1.5</dt>\n",
       "\t\t<dd>1</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$mean] 13.8145687726395\n",
       "\\item[\\$sd] 2.16623011963433\n",
       "\\item[\\$quantile.02] 9.55368421000001\n",
       "\\item[\\$p.upper.1.5] 1\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$mean\n",
       ":   13.8145687726395\n",
       "$sd\n",
       ":   2.16623011963433\n",
       "$quantile.02\n",
       ":   9.55368421000001\n",
       "$p.upper.1.5\n",
       ":   1\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$mean\n",
       "[1] 13.81457\n",
       "\n",
       "$sd\n",
       "[1] 2.16623\n",
       "\n",
       "$quantile.02\n",
       "[1] 9.553684\n",
       "\n",
       "$p.upper.1.5\n",
       "[1] 1\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ApproximateParameter(rayleigh.sample$stand.by)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Para el caso de la configuración de componentes en modo \"stand by\", la duración del dispositivo es muy alta (como era de esperar), siendo mayor que 10 años con probabilidad alta (ya que el cuantil 0.02 se encuentra casi en dicho valor). Por estas razones, la probabilidad de que el dispositivo dure más de un año es técnicamente un suceso seguro."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado B.4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se utilizarán los datos transformados en el [Apartado A.4](#Apartado-A.4), y referidos a *La duración del dispositivo si los componentes están acoplados de tal forma que **el dispositivo funciona mientras al menos seis de los componentes estén en funcionamiento**.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$mean</dt>\n",
       "\t\t<dd>1.19043357233194</dd>\n",
       "\t<dt>$sd</dt>\n",
       "\t\t<dd>0.248675222239707</dd>\n",
       "\t<dt>$quantile.02</dt>\n",
       "\t\t<dd>0.722444299705511</dd>\n",
       "\t<dt>$p.upper.1.5</dt>\n",
       "\t\t<dd>0.112133333333333</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$mean] 1.19043357233194\n",
       "\\item[\\$sd] 0.248675222239707\n",
       "\\item[\\$quantile.02] 0.722444299705511\n",
       "\\item[\\$p.upper.1.5] 0.112133333333333\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$mean\n",
       ":   1.19043357233194\n",
       "$sd\n",
       ":   0.248675222239707\n",
       "$quantile.02\n",
       ":   0.722444299705511\n",
       "$p.upper.1.5\n",
       ":   0.112133333333333\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$mean\n",
       "[1] 1.190434\n",
       "\n",
       "$sd\n",
       "[1] 0.2486752\n",
       "\n",
       "$quantile.02\n",
       "[1] 0.7224443\n",
       "\n",
       "$p.upper.1.5\n",
       "[1] 0.1121333\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ApproximateParameter(rayleigh.sample$least.6) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En esta configuración, nos encontramos en un caso intermedio entre los dos anterior (componentes conectados en serie y los componentes conectados en paralelo), lo cual que se refleja en cierta manera en la forma de la distribución obtenida."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado B.5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se utilizarán los datos transformados en el [Apartado A.5](#Apartado-A.5), y referidos a *La **duración promedio de los once componentes** si se supone que todos comienzan su funcionamiento a la vez y el dispositivo se mantiene activo hasta que todos han fallado.*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<dl>\n",
       "\t<dt>$mean</dt>\n",
       "\t\t<dd>1.25586988842177</dd>\n",
       "\t<dt>$sd</dt>\n",
       "\t\t<dd>0.196930010875848</dd>\n",
       "\t<dt>$quantile.02</dt>\n",
       "\t\t<dd>0.868516746363638</dd>\n",
       "\t<dt>$p.upper.1.5</dt>\n",
       "\t\t<dd>0.107466666666667</dd>\n",
       "</dl>\n"
      ],
      "text/latex": [
       "\\begin{description}\n",
       "\\item[\\$mean] 1.25586988842177\n",
       "\\item[\\$sd] 0.196930010875848\n",
       "\\item[\\$quantile.02] 0.868516746363638\n",
       "\\item[\\$p.upper.1.5] 0.107466666666667\n",
       "\\end{description}\n"
      ],
      "text/markdown": [
       "$mean\n",
       ":   1.25586988842177\n",
       "$sd\n",
       ":   0.196930010875848\n",
       "$quantile.02\n",
       ":   0.868516746363638\n",
       "$p.upper.1.5\n",
       ":   0.107466666666667\n",
       "\n",
       "\n"
      ],
      "text/plain": [
       "$mean\n",
       "[1] 1.25587\n",
       "\n",
       "$sd\n",
       "[1] 0.19693\n",
       "\n",
       "$quantile.02\n",
       "[1] 0.8685167\n",
       "\n",
       "$p.upper.1.5\n",
       "[1] 0.1074667\n"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ApproximateParameter(rayleigh.sample$mean)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se está estudiando el tiempo promedio de los componentes, lo cual nos permite conocer más en detalle la duración de cada uno de ellos. Sin embargo, en este caso no nos podemos fijar en la desviación estándar de los datos, ya que está sesgada por el número de componentes promediados. Estudiando los valores de los parámetros sabemos que el tiempo promedio de duración de un componente es de un año y cuatro meses, así como que la decima parte de ellos no dura más de un año y medio."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apartado C"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "El enunciado del apartado es:\n",
    "\n",
    "*Para los casos descritos en los apartados [A.1](#Apartado-A.1) y [A.2](#Apartado-A.2), obtener también una expresión analítica de la función de densidad de las variables siguiendo las indicaciones dadas en el material de *del Barrio & Gordaliza* en el capítulo \"Modelos de fiabilidad. La ley de Weibull\". Hacer una representación de dichas funciones superpuestas sobre los histogramas obtenidos por las simulaciones de Montecarlo.*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado C.1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se va a estudiar el supuesto en el [Apartado A.1](#Apartado-A.1), el cual se refiere a la elección de una configuración en serie. Tal y como indicamos en dicho apartado, esto se refiere a la búsqueda del componente de menor duracción. Es decir,\n",
    "\n",
    "Sea:\n",
    "$$\n",
    "X_1, ..., X_{n} \\ v.a.i.i.d. \\ | \\ X_i \\sim Rayleigh(\\sigma)\n",
    "$$\n",
    "\n",
    "Entonces nuestra variable de estudio es: \n",
    "\n",
    "\\begin{align}\n",
    "X_S \n",
    "&= min\\left(\\left\\{X_1, ..., X_{11}\\right\\}\\right) \\\\\n",
    "&= X_{(1)}\n",
    "\\end{align}\n",
    "\n",
    "Como sabemos:\n",
    "\n",
    "\\begin{align}\n",
    "F_S(x) \n",
    "&= F_{X_{(1)}}\\left( x \\right) \\\\\n",
    "&= 1 - \\left(1 - F_{X_i}\\left(x\\right) \\right) ^ n \\\\\n",
    "&= 1 - \\left(1 - \\left(1 - exp\\left( - \\frac{x ^ 2}{2 \\sigma ^ 2}\\right) \\right) \\right) ^ n \\\\\n",
    "&= 1 - exp\\left(-\\frac{nx^2}{2\\sigma^2}\\right)\n",
    "\\end{align}\n",
    "\n",
    "Ahora calculamos la función de densidad simplemente derivando la función de distribución obtenida:\n",
    "\n",
    "\\begin{align}\n",
    "f_S(x) \n",
    "&= \\frac{\\partial}{\\partial x} F_S(x) \\\\\n",
    "&= \\frac{\\partial}{\\partial x} 1 - exp\\left(-\\frac{nx^2}{2\\sigma^2}\\right) \\\\\n",
    "&= \\frac{nx}{\\sigma^2} \\cdot exp\\left(-\\frac{nx^2}{2\\sigma^2}\\right)\n",
    "\\end{align}\n",
    "\n",
    "Si nos paramos a estudiar la relación entre esta variable y la de las variables de partida no es difícil darse cuenta de que:\n",
    "\n",
    "$$\n",
    "X_{S} \\sim Rayleigh\\left(\\frac{\\sigma}{\\sqrt{n}}\\right)\n",
    "$$\n",
    "\n",
    "Para nuestro caso en particular tenemos que:\n",
    "\n",
    "$$\n",
    "X_{S} \\sim Rayleigh\\left(\\frac{1}{\\sqrt{11}}\\right)\n",
    "$$\n",
    "\n",
    "Por tanto, tan solo tendremos que cambiar el parámetro sigma por su valor adecuado."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación se muestra una representación gráfica del histograma de la variable junto con la sobreposición de la función de densidad desarrollada de manera analítica en el párrafo anterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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XX7nkCAgTAQSCWUBbmw0ZMqQkuaEWrVu3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\nELBX4P8BqUmy2m5rQ6cAAAAASUVORK5CYII=",
      "text/plain": [
       "plot without title"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "rayleigh.sample %>%\n",
    "    ggplot(aes(x = series)) +\n",
    "        scale_x_continuous(limits = x.limits) + \n",
    "        geom_histogram(aes(y = ..density..), binwidth = 0.1) +\n",
    "        stat_function(fun = rayleigh.density, args = list(sigma = 1 / sqrt(n.c)), col = \"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Apartado C.2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso se va a estudiar el supuesto en el [Apartado A.2](#Apartado-A.2), el cual se refiere a la elección de una configuración en serie. Tal y como indicamos en dicho apartado, esto se refiere a la búsqueda del componente de menor duracción. Es decir,\n",
    "\n",
    "Sea:\n",
    "$$\n",
    "X_1, ..., X_{n} \\ v.a.i.i.d. \\ | \\ X_i \\sim Rayleigh(\\sigma)\n",
    "$$\n",
    "\n",
    "Entonces nuestra variable de estudio es: \n",
    "\n",
    "\\begin{align}\n",
    "X_P \\\\\n",
    "&= max\\left(\\left\\{X_1, ..., X_{11}\\right\\}\\right) \\\\\n",
    "&= X_{(n)}\n",
    "\\end{align}\n",
    "\n",
    "Como sabemos:\n",
    "\n",
    "\\begin{align}\n",
    "F_P(x) \n",
    "&= F_{ X_{(n)} } \\left( x \\right) \\\\\n",
    "&= \\left( F_{X_i} \\left( x \\right) \\right) ^ n \\\\\n",
    "&= \\left(1 - exp\\left( - \\frac{x ^ 2}{2 \\sigma ^ 2}\\right) \\right) ^ n\n",
    "\\end{align}\n",
    "Ahora calculamos la función de densidad simplemente derivando la función de distribución obtenida:\n",
    "\n",
    "\\begin{align}\n",
    "f_P(x) \n",
    "&= \\frac{\\partial}{\\partial x} F_P(x) \\\\\n",
    "&= \\frac{\\partial}{\\partial x} \\left(F_{X_i}\\left(x\\right) \\right) ^ n \\\\\n",
    "&= n \\ f_{X_i}\\left(x\\right) \\left(F_{X_i}\\left(x\\right) \\right) ^ {n - 1}  \\\\\n",
    "&= \\frac{n x}{\\sigma^2}exp\\left(-\\frac{x^2}{2\\sigma^2}\\right) \\left(1 -exp\\left(-\\frac{x^2}{2\\sigma^2}\\right)\\right) ^ {n - 1}\n",
    "\\end{align}\n",
    "\n",
    "En este caso no parece surgir ninguna función conocida a partir de la transformación. A continuación se incluye el código *R* necesario para la implementación de la función:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "rayleigh.max.density <- function(x, sigma = 1, n = 11) {\n",
    "   n * rayleigh.density(x) * rayleigh.distribution(x) ^ (n - 1)\n",
    "}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación se muestra una representación gráfica del histograma de la variable junto con la sobreposición de la función de densidad desarrollada de manera analítica en el párrafo anterior:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {},
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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WDzeOSlgX3Fk5ra8pAhXgfz86TuV78Q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\ne+Y+p8L5f1P5eecobtPXanfr7eow9ASl3XWfYjd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      "text/plain": [
       "plot without title"
      ]
     },
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   ],
   "source": [
    "rayleigh.sample %>%\n",
    "    ggplot(aes(x = parallel)) +\n",
    "        scale_x_continuous(limits = x.limits) + \n",
    "        geom_histogram(aes(y = ..density..), binwidth = 0.1) +\n",
    "        stat_function(fun = rayleigh.max.density, col = \"red\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusiones\n",
    "\n",
    "En este trabajo se ha podido comprobar la potencia de la *transformación cuantil* para simulación de variables, lo cual se conoce como el método de *Monte Carlo*. Esta estrategia de simulación permite generar muestras de cualquier distribución conocida de tal manera que ningún método conocido permita distinguir entre observaciones reales de la distribución y las aquí simuladas. \n",
    "\n",
    "Gracias a métododos de simulación como el aquí estudiado es fácil darse cuenta del gran ahorro económico que se puede tiene frente a simulaciones físicas, cuyas dificultades a nivel del tiempo necesario para ser llevadas a cabo es en muchas situaciones impracticable. Otras circunstancias en que los métodos de simulación suponen ventajas frente a métodos analíticos son aquellos en que el suceso de estudio es complicado de desarrollar por dicha vía (o incluso imposible debido a dificultades matemáticas). Por tanto, existen un gran número de ocasiones en que los métodos de simulación otorgan una buena aproximación al comportamiento real de ciertos fenómenos.\n",
    "\n",
    "En cuanto a la distribución simulada en este caso, las variables de *Rayleigh* se utilizan para modelizar fenómenos de duración del tiempo de vida de determinados componentes físicos, ya sean materiales o incluso biológicos, por lo que es enriquecedor conocer y manejar dicha distribución."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Referencias\n",
    "  * [WI09] H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2009.\n",
    "  * [WI11] Hadley Wickham (2011). The Split-Apply-Combine Strategy for Data Analysis. Journal of Statistical Software, 40(1), 1-29. URL http://www.jstatsoft.org/v40/i01/. \n",
    "  * [BA12] Baptiste Auguie (2012). gridExtra: functions in Grid graphics. R package version 0.9.1. http://CRAN.R-project.org/package=gridExtra \n",
    "  * [TRC13] R Core Team (2013). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL http://www.R-project.org/.\n",
    "  * [SA18] Del Barrio & Gordaliza. Modelos Probabilísticos, 2017/18. Facultad de Ciencias: Departamento de Estadística e Investigación Operativa."
   ]
  }
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