lln.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Teoremas \"límite\" de la Estadística: Ley de los Grandes Números (LLN: Large Numbers Law) (1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introducción"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Cuando pensamos en repeticiones de eventos aleatorios (tirar una moneda al aire por ejemplo, o cuando oímos las distribuciones de la terminación de la lotería ) la intuición nos dice que cuanto más mayor sea ese número de repeticiones más a salvo estaremos de situaciones \"anómalas\".\n",
    "\n",
    "Si disponemos de una moneda y la lanzamos al aire sabemos que (¡siempre que sea una moneda \"fiel\"!) tanto la cara como la cruz disponen de una probabilidad del 50% de que ocurran. Pero si repetimos ese experimento muchas veces: ¿qué posibilidades tenemos de que la media se aleje de ese teórico 50%?. La intuición nos dice que a larga, y con un número suficiente de repeticiones del experimiento, nos iremos acercando a ese 50%, y esas situaciones anómalas se irán disipando. ¿Pero con qué probabilidad?, ¿cómo se realiza esa convergencia? ¿como se comporta la media conforme aumentamos el número de experimentos?.\n",
    "\n",
    "Vamos a estudiar estos conceptos por medio de dos teóremas fundamentales de la Estadística: La Ley de los Grandes Números y el Teorema del Límite Central. En este post hablaremos del primero.\n",
    "\n",
    "Vamos a apoyarnos en distribuciones Binomiales y de Bernouilli, por lo que dedicaremos unas líneas a ellas, y además introduciremos el Teorema de Markov y el Teorema de Chebyshev, necesarios para la demostración del Teorema protagonista de este post."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribución de Bernouilli"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es esta una distribución de probabilidad de variable aleatoria en la que definimos un éxito, $valor=1$,  con una probabilidad $p$ y un fracaso, $valor=0$, con probabilidad $q=1-p$. Ejemplo o caso práctico es el mencionado en la introducción: lanzamiento de moneda con $p=1/2$. \n",
    "\n",
    "Calculemos el valor esperado y la varianza de esta distribución que usaremos estos valores posteriormente:\n",
    "\n",
    "$E[X]=\\sum_x x*p(x)=1*p+0*q=p $\n",
    "\n",
    "$Var[X]=|E[X^2]\\,-E[X]^2|=1^2p+0*q-pp=p-p^2=p(1-p)$\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " ## Distribución binomial"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En el caso de que repitamos experimentos basados en la distribución anterior nos encontraremos con una distribución binomial. \n",
    "\n",
    "La caracterizaremos por un valor $p$, probabilidad de éxito, y un valor $n$, número de experimentos realizados. Formalmente una variable aleatoria con distribución binomial la representaremos tal que $X\\sim B(n,p)$. $X$ marca el número de éxitos tras los $n$ intentos o experimentos.\n",
    "\n",
    "La función de densidad de probabilidad es:\n",
    "\n",
    "$f(x)={n\\choose k} p^k  (1-p)^{n-k}$, con $k\\in\\{0..n\\}$\n",
    "\n",
    "y con un valor esperado $E(X)=np$ y una varianza $Var(X)=np(1-p)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Desigualdad de Markov"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "La desigualdad de Markov nos dice que siendo $X$ una variable aleatoria, con valores siempre mayor o igual que cero, entonces:\n",
    "\n",
    "$P(X\\geq a)\\leq \\dfrac {E[X]}{a} \\;  \\forall a > 0$ \n",
    "\n",
    "Veamos una rápida demostración. Para ello definimos una variable auxiliar $I$, tal que:\n",
    "$\n",
    "I=\\left\\{\n",
    "                \\begin{array}{ll}\n",
    "                  1 \\; si X \\geq a\\\\\n",
    "                  0 \\;resto\n",
    "                \\end{array}\n",
    "              \\right.\n",
    "$ lo cual implica que $I \\leq \\dfrac{X}{a} $. Aplicamos ahora valor esperado a ambos lados:\n",
    "$E[I] \\leq \\dfrac {E[X]}{a}$, y aplicando la definición de valor esperado: $E[\\mathrm{X}]=\\sum _{x\\in \\mathrm{X}} x*p(x)=1*p(X\\geq a) + 0*p(X<a)$ luego $E[I]=p(X \\geq a)$ con lo que $p(X\\geq a) \\leq \\dfrac {E[X]}{a}$ $\\blacksquare$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Desigualdad de Chebyshev´s"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esta desigualdad nos dice que siendo $X$ una variable aleatoria con una media finita $\\mu$ y una varianza $\\sigma^2$, entonces $\\forall k >0$ : \n",
    "\n",
    "$p\\left(\\left| x-\\mu \\right| \\geq k\\right) \\leq \\dfrac {\\sigma^2}{k^2}$\n",
    "\n",
    "Efectivamente, si aplicamos $Markov$ con $k^2=a$ entonces: \n",
    "\n",
    "$p\\left\\{(x-\\mu)^2\\geq k^2  \\right\\}\\leq\\dfrac{E\\left[(x-\\mu)^2\\right]}{k^2}$ y de ahí se infiere que: \n",
    "$p\\left\\{(x-\\mu)\\geq k  \\right\\}\\leq\\dfrac{\\sigma^2}{k^2}$  $\\blacksquare$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ley \"débil\" de los Grandes Números"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esta desigualdad nos dice que siendo $X_1, X_2,\\cdots,X_n$ variables \n",
    "aleatorias independientes e idénticamente distribuidas (nos referiremos a este hecho como $i.i.d.$) con media finita $\\mathrm{E}\\left[x_i\\right]=\\mu$ y varianza finita $\\sigma^2$, entonces $\\forall \\epsilon >0$ se cumple que  $p\\left\\{\\left| \\dfrac {x_1+\\cdots+x_n}{n} - \\mu\\right| \\geq \\epsilon\\right\\} \\rightarrow 0$ cuando $n\\rightarrow \\infty$. Esta ley nos indica, de manera resumida, que la media de las estimaciones de una variable $X$ tiende a la media de esa variable.\n",
    "\n",
    "Para probar este teorema partimos del hecho de que $\\mathrm{E}\\left[\\dfrac{X_1+\\cdots+X_n}{n}\\right]=n\\mu/n=\\mu$ y que $Var\\left(\\dfrac{X_1+\\cdots+X_n}{n}\\right)=\\dfrac{\\sigma^2}{n}$ (ambos se extraen de las definiciones de valor esperado y varianza), y podemos aplicar la desigualdad de Chebyshev tal que:\n",
    "\n",
    "$$\n",
    "p\\left\\{\\left|\\dfrac{X_1+\\cdots+X_n}{n}\\right|-\\mu)\\geq \\epsilon \\right\\}\\leq\\dfrac{\\sigma^2}{nk^2}$$ y como $n\\rightarrow\\infty$ entonces el término de la derecha tiende a cero con lo que queda demostrado.\n",
    "\n",
    "Hemos visto aquí el primero de los tres teoremas, nos demuestra lo que de manera intuitiva entendemos: la media de los valores estimados de una variable se acercará a la media teórica de esa variable aleatoria cuanto más valores estimemos.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Juguemos con Python y con estos conceptos "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vamos a realizar simulaciones y comprobar como se cumplen el resultado previsto en el LLN.\n",
    "\n",
    "Para ello jugaremos con las librerías scipy, para las herramientas estadísticas, y con la clásica matplotlib para los gráficos.\n",
    "\n",
    "Empecemos con la importación:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.ticker import PercentFormatter"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Jugaremos con las dos distribuciones que hemos visto en el comienzo de este artículo: la de Bernouilli y su repetición: la Binomial. Nos basaremos en la función [np.random.binomial](https://docs.scipy.org/doc/numpy-1.14.0/reference/generated/numpy.random.binomial.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "valor1=[1] y valor2=[0]\n"
     ]
    }
   ],
   "source": [
    "p=q=1/2\n",
    "valor1=np.random.binomial(1,p,1)\n",
    "valor2=np.random.binomial(1,p,1)\n",
    "print ('valor1={} y valor2={}'.format(valor1,valor2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estos dos son ejemplos de Bernouilli, realizamos el experimento de \"lanzamiento de moneda\" (hemos elegido una $p=1/2$) una sola vez.\n",
    "\n",
    "Podemos también realizar ese experimento n veces y ver la media:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5]\n"
     ]
    }
   ],
   "source": [
    "valor3=np.random.binomial(n=10,p=p,size=1)\n",
    "print (valor3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este caso vemos el sumatorio de los n experimentos (un nº entre 0 y 10), si lo dividimos entre n obtendremos la media de esos experimentos que será un número entre 0 y 1:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.4]\n"
     ]
    }
   ],
   "source": [
    "n=10\n",
    "valor4=np.random.binomial(n=n,p=p,size=1)/n\n",
    "print (valor4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Repitamoslo varias veces:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.5]\n",
      "[0.7]\n",
      "[0.6]\n",
      "[0.6]\n",
      "[0.3]\n"
     ]
    }
   ],
   "source": [
    "n=10\n",
    "for i in range(5):\n",
    "    valor4=np.random.binomial(n=n,p=p,size=1)/n\n",
    "    print (valor4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Esta misma repetición la podemos conseguir de manera más simple con el parámetro size. Obtendremos un array de numpy de dimensiones (size,)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.8 0.7 0.5 0.4 0.2]\n"
     ]
    }
   ],
   "source": [
    "valor5=np.random.binomial(n=n,p=p,size=5)/n\n",
    "print (valor5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ya tenemos entonces un método para hacer simulación de sumas de variables aleatorias. Se compondrá de resultados de realizar el experimento 'n' veces, hallando su media si fuera necesarios al dividir por 'n', y realizaremos esa observación 'size' veces. Por ejemplo: el experimento se compone de 50 lanzamientos de una moneda hallando posteriormente la suma de los valores, y realizaremos ese experimento 100 veces."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[26 24 31 28 28 26 23 29 25 20 31 25 26 22 28 24 23 23 23 28 21 27 19 28\n",
      " 19 26 30 28 28 21 23 27 21 23 24 28 29 20 25 24 27 24 34 28 18 25 27 30\n",
      " 27 24 28 20 27 23 24 26 28 19 28 28 26 29 26 29 29 20 23 28 30 29 20 23\n",
      " 25 25 21 22 20 16 31 25 33 26 28 24 22 27 27 23 23 24 28 28 24 24 33 28\n",
      " 24 29 26 19]\n",
      "[0.52 0.48 0.62 0.56 0.56 0.52 0.46 0.58 0.5  0.4  0.62 0.5  0.52 0.44\n",
      " 0.56 0.48 0.46 0.46 0.46 0.56 0.42 0.54 0.38 0.56 0.38 0.52 0.6  0.56\n",
      " 0.56 0.42 0.46 0.54 0.42 0.46 0.48 0.56 0.58 0.4  0.5  0.48 0.54 0.48\n",
      " 0.68 0.56 0.36 0.5  0.54 0.6  0.54 0.48 0.56 0.4  0.54 0.46 0.48 0.52\n",
      " 0.56 0.38 0.56 0.56 0.52 0.58 0.52 0.58 0.58 0.4  0.46 0.56 0.6  0.58\n",
      " 0.4  0.46 0.5  0.5  0.42 0.44 0.4  0.32 0.62 0.5  0.66 0.52 0.56 0.48\n",
      " 0.44 0.54 0.54 0.46 0.46 0.48 0.56 0.56 0.48 0.48 0.66 0.56 0.48 0.58\n",
      " 0.52 0.38]\n"
     ]
    }
   ],
   "source": [
    "n=50\n",
    "valor6=np.random.binomial(n=n,p=p,size=100)\n",
    "valor6_medios=valor6/n\n",
    "print (valor6)\n",
    "print (valor6_medios)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Y podemos calcular la media de esos experimentos y la desviación estándar de los resultados, Frente a unos valores teóricos de media=p*n y varianza=p(1-p)n, según hemos visto "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valores reales de la muestra: Media=25.36, Varianza=12.65\n",
      "Valores teóricos:             Media=25.00, Varianza=12.50\n"
     ]
    }
   ],
   "source": [
    "print ('Valores reales de la muestra: Media={:.2f}, Varianza={:.2f}'.format(valor6.mean(),valor6.std()**2))\n",
    "print ('Valores teóricos:             Media={:.2f}, Varianza={:.2f}'.format(p*n,p*(1-p)*n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "De igual manera podemos ver la media y varianza de las medias de las sumas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Valores reales de la muestra: Media=0.5072, Varianza=0.00506\n",
      "Valores teóricos:             Media=0.5000, Varianza=0.00500\n"
     ]
    }
   ],
   "source": [
    "print ('Valores reales de la muestra: Media={:.4f}, Varianza={:.5f}'.format(valor6_medios.mean(),\n",
    "                                                                            valor6_medios.std()**2))\n",
    "print ('Valores teóricos:             Media={:.4f}, Varianza={:.5f}'.format(p,p*(1-p)/n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "En este punto vamos a crear una función que genere este tipo de resultados, le pasaremos como parámetros: nº de términos a sumar (n), la probabilidad p y el nº de observaciones que queremos que nos devuelva. Con la particularidad de que la n (términos a sumar) podrá ser una lista, de tal manera que, de manera fácil, podamos ver la evolución de la media conforme vamos aumentando el nº de sumandos. Esta función `generador_binomial` nos devolverá un diccionario cuyos índices serán cada uno de los elementos de la lista `terminos_a_sumar` y como valores la lista de las observaciones,junto con la varianza teórica, la media y la varianza de las observaciones."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def generador_binomial(terminos_a_sumar,p,numero_de_observ):\n",
    "    media=[]\n",
    "    varianza=[]\n",
    "    series={}\n",
    "    varianza_base=p*(1-p)      \n",
    "    var_teorica=[]\n",
    "    for n in terminos_a_sumar:\n",
    "        valores=np.random.binomial(n,0.5,numero_de_observ)/n\n",
    "        media.append(valores.mean())\n",
    "        var_teorica.append(varianza_base/n)\n",
    "        varianza.append(valores.std()**2)\n",
    "        series[n]=valores\n",
    "    return series,var_teorica,media,varianza"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "preparemos una lista con varios escenarios: cada nº representa una `n`, número de términos a sumar para calcular posteriormente la media. Usaremos nueve para cuadrar posteriormente los gráficos. A continuación llamaremos a la función, solicitando 1000 observaciones:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "lista_terms_sum=[10,50,100,200,300,400,500,1000,10000] #han de ser 9!\n",
    "#lista_terms_sum=[10,100,500,1000,5000,10000,50000,100000,1000000]\n",
    "#lista_terms_sum=[10,20,30,40,50,60,70,80,90]\n",
    "series,var_teorica,media,varianza=generador_binomial(lista_terms_sum,p=1/2,numero_de_observ=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A continuación representaremos gráficamente estas 1000 observaciones, y veremos el efecto del teorema LLN conforme aumentamos el nº de términos en la suma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x720 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "f = plt.figure(figsize=(10,10))\n",
    "f.subplots_adjust(hspace=1, wspace=1)\n",
    "ax1 = f.add_subplot(331)\n",
    "ax2 = f.add_subplot(332)\n",
    "ax3 = f.add_subplot(333)\n",
    "ax4 = f.add_subplot(334)\n",
    "ax5 = f.add_subplot(335)\n",
    "ax6 = f.add_subplot(336)\n",
    "ax7= f.add_subplot(337)\n",
    "ax8= f.add_subplot(338)\n",
    "ax9= f.add_subplot(339)\n",
    "f.subplots_adjust(hspace=.5, wspace=0.5)\n",
    "lista_axes=f.get_axes()\n",
    "N_bins=np.linspace(0,1,100)\n",
    "n_decimales=2\n",
    "for i in range(0,9):\n",
    "    lista_axes[i].set_xlabel('{:,} términos en la suma'.format(lista_terms_sum[i]))\n",
    "    lista_axes[i].yaxis.set_major_formatter(PercentFormatter(1))\n",
    "    lista_axes[i].set_xlim(0.2,0.8)\n",
    "    lista_axes[i].set_ylim(0.0,0.25)\n",
    "    counts, bins = np.histogram(np.around(series[lista_terms_sum[i]],decimals=n_decimales),bins=N_bins)\n",
    "    lista_axes[i].hist(bins[:-1],bins,weights=counts/counts.sum())\n",
    "    lista_axes[i].text(0.0,0.8,'Varianza muestra={:.4}'.\n",
    "                       format(varianza[i]),transform=lista_axes[i].transAxes,color='tab:orange')\n",
    "    lista_axes[i].text(0.0,0.6,'Varianza teórica={:.4}'.\n",
    "                       format(var_teorica[i]),transform=lista_axes[i].transAxes,color='tab:orange')\n",
    "    lista_axes[i].text(0.0,0.4,'Media de la muestra={:.4}'.\n",
    "                       format(media[i]),transform=lista_axes[i].transAxes,color='tab:orange')\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Podemos observar como la varianza disminuye como nos indica la teoría (inversamente proporcial a n) y la media converge a la media de la variable aleatoria inicial. Vemos mejor este efecto con el gráfico siguiente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax1 = plt.subplots()\n",
    "color = 'tab:red'\n",
    "ax1.set_xscale('log', basex=10)\n",
    "ax1.set_xlabel('Nº términos en la suma')\n",
    "ax1.set_ylabel('Varianza', color=color)\n",
    "ax1.set_ylim(0,0.03)\n",
    "ax1.plot(lista_terms_sum,varianza, color=color)\n",
    "ax1.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "ax2 = ax1.twinx() \n",
    "\n",
    "color = 'tab:blue'\n",
    "ax2.set_ylabel('media', color=color)  \n",
    "ax2.plot(lista_terms_sum,media, color=color)\n",
    "ax2.tick_params(axis='y', labelcolor=color)\n",
    "\n",
    "fig.tight_layout()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conclusiones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hemos visto la base teórica que rigue el comportamiento de variables aleatorias cuando realizas experimentos un número elevado de veces, para, a continuación, realizar simulaciones en `python`, utilizando librerias de uso común, para confirmar que obtenemos resultados alineados con la teoría. En un próximo post veremos el Teorema Central del Límite."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notebook y código disponible en mi repositorio [github](https://github.com/mharias/stats) en https://github.com/mharias/stats"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}