practicos/soluciones/05_guia_soluciones.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Práctico 5: Generación de Variables Aleatorias Continuas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algoritmos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import random as rnd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "\n",
    "from time import time\n",
    "from scipy import stats as st"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de la Transformada Inversa"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def inverse_transform_method(G: callable) -> float:\n",
    "    \"\"\"\n",
    "    Inverse Transform Method for generating random numbers from a given distribution.\n",
    "\n",
    "    Parameters:\n",
    "    G: callable\n",
    "        The inverse of the cumulative distribution function of the distribution from which we want to generate random numbers.\n",
    "\n",
    "    Returns:\n",
    "    float\n",
    "        A random number from the distribution.\n",
    "    \"\"\"\n",
    "    U = rnd.random()\n",
    "    return G(U)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generación de VAs Poisson"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected mean: 2 and variance: 2\n",
      "Actual mean: 1.99855 and variance: 2.0150878975000004\n"
     ]
    }
   ],
   "source": [
    "def poisson_distribution(l: float, sz: int = 1) -> list[int]:\n",
    "    \"\"\"\n",
    "    Generates random numbers from a Poisson distribution.\n",
    "\n",
    "    Parameters:\n",
    "    l: float\n",
    "        The rate parameter of the Poisson distribution.\n",
    "    sz: int\n",
    "        The number of random numbers to generate.\n",
    "\n",
    "    Returns:\n",
    "    list[int]\n",
    "        A list of random numbers from the Poisson distribution.\n",
    "    \"\"\"\n",
    "    def generate(l: float) -> int:\n",
    "        x = 0; p = 1 - rnd.random(); lim = np.exp(-l)\n",
    "        while p >= lim: p *= 1 - rnd.random(); x += 1\n",
    "        return x\n",
    "        \n",
    "    return [generate(l) for _ in range(sz)]\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    # Check if the generated random numbers are from the Poisson distribution.\n",
    "    l = 2\n",
    "    sz = 10**5\n",
    "    random_numbers = poisson_distribution(l, sz)\n",
    "    print(f\"Expected mean: {l} and variance: {l}\")\n",
    "    print(f\"Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generación de VAs Gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected mean: 4 and variance: 8\n",
      "Actual mean: 3.9952478626527763 and variance: 8.009654102848492\n"
     ]
    }
   ],
   "source": [
    "def gamma_distribution(a: int, b: float, sz: int = 1) -> list[float]:\n",
    "    \"\"\"\n",
    "    Generates random numbers from a gamma distribution with shape parameter ('a') as integer.\n",
    "\n",
    "    Parameters:\n",
    "    a: int\n",
    "        The shape parameter of the gamma distribution.\n",
    "    b: float\n",
    "        The rate parameter of the gamma distribution.\n",
    "    sz: int\n",
    "        The number of random numbers to generate.\n",
    "\n",
    "    Returns:\n",
    "    list[float]\n",
    "        A list of random numbers from the gamma distribution.\n",
    "    \"\"\"\n",
    "    def generate_gamma(a: int, b: float) -> float:\n",
    "        u = 1\n",
    "        for _ in range(a): u *= 1 - rnd.random()\n",
    "        assert u > 0, \"Invalid value generated for u\"\n",
    "        return -np.log(u) * b\n",
    "\n",
    "    return [generate_gamma(a, b) for _ in range(sz)]\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    # Check if the generated random numbers are from the gamma distribution.\n",
    "    a = 2; b = 2\n",
    "    sz = 10**5\n",
    "    random_numbers = gamma_distribution(a, b, sz)\n",
    "    print(f\"Expected mean: {a * b} and variance: {a * b ** 2}\")\n",
    "    print(f\"Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generación de VAs Exponenciales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected mean: 0.5 and variance: 0.25\n",
      "With Gamma method:\n",
      "    Actual mean: 0.5147513918285718 and variance: 0.2398663399772217\n",
      "With Inverse Transform method:\n",
      "    Actual mean: 0.5017849777881859 and variance: 0.247495447834776\n"
     ]
    }
   ],
   "source": [
    "def exponential_distribution(l: float, sz: int = 1, gamma_method: bool = True) -> list[float]:\n",
    "    \"\"\"\n",
    "    Generates random numbers from an exponential distribution.\n",
    "\n",
    "    Parameters:\n",
    "    l: float\n",
    "        The rate parameter of the exponential distribution.\n",
    "    sz: int\n",
    "        The number of random numbers to generate.\n",
    "    gamma_method: bool\n",
    "        If True, uses the gamma distribution method to generate random numbers. Otherwise, uses the inverse transform method.\n",
    "        (The gamma method is more efficient for generating multiple random numbers but if the SZ is big, -log(u) can be very close to 0 and cause numerical issues.)\n",
    "\n",
    "    Returns:\n",
    "    list[float]\n",
    "        A list of random numbers from the exponential distribution.\n",
    "    \"\"\"\n",
    "    if sz == 1 or not gamma_method:\n",
    "        return [inverse_transform_method(lambda u: -np.log(1 - u) / l) for _ in range(sz)]\n",
    "\n",
    "    # Method using a Gamma distribution.\n",
    "    t = gamma_distribution(sz, 1/l)[0]\n",
    "    u = sorted([rnd.random() for _ in range(sz - 1)] + [0, 1])\n",
    "    return [(u[i] - u[i-1]) * t for i in range(1, len(u))]\n",
    "\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    # Check if the generated random numbers are from the exponential distribution.\n",
    "    l = 2\n",
    "    print(f\"Expected mean: {1 / l} and variance: {1 / l ** 2}\")\n",
    "    \n",
    "    print(f\"With Gamma method:\")\n",
    "    sz = 600\n",
    "    random_numbers = exponential_distribution(l, sz)\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "\n",
    "    print(f\"With Inverse Transform method:\")\n",
    "    sz = 10**4\n",
    "    random_numbers = exponential_distribution(l, sz, gamma_method=False)\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de Aceptación y Rechazo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Rejection Method:\n",
      "    Expected mean: 1.5 and variance: 1.5\n",
      "    Actual mean: 1.4976184631986877 and variance: 1.4969492699997708\n",
      "Using Transform Rejection Method:\n",
      "    Expected mean: 1.5 and variance: 1.5\n",
      "    Actual mean: 1.5018764329686778 and variance: 1.4980081413413486\n"
     ]
    }
   ],
   "source": [
    "def rejection_method(Y: callable, p: callable, q: callable, c: float, sz: int = 1) -> list[float]:\n",
    "    \"\"\"\n",
    "    Estimate the expected value of a function using the rejection method.\n",
    "\n",
    "    Parameters:\n",
    "    Y: callable - Function to simulate the random variable.\n",
    "    p: callable - Probability function of the random variable of X.\n",
    "    q: callable - Probability function of the random variable of Y.\n",
    "    c: float - Constant such that p(x) <= c * q(x) for all x.\n",
    "    sz: int - Number of random numbers to generate.\n",
    "\n",
    "    Returns:\n",
    "    list[int] - List of random numbers.\n",
    "    \"\"\"\n",
    "    def generate(Y: callable, p: callable, q: callable, c: float) -> float:\n",
    "        while True:\n",
    "            x = Y()\n",
    "            U = rnd.random()\n",
    "            if U < p(x) / (c * q(x)): return x\n",
    "    \n",
    "    return [generate(Y, p, q, c) for _ in range(sz)]\n",
    "\n",
    "def transform_rejection_method(H: callable, Hd: callable, p: callable, c: float, sz: int = 1) -> list[float]:\n",
    "    \"\"\"\n",
    "    Estimate the expected value of a function using the rejection method.\n",
    "\n",
    "    Parameters:\n",
    "    H: callable - Inverse of the cumulative distribution function of the random variable of Y.\n",
    "    Hd: callable - Derivative of H.\n",
    "    p: callable - Probability function of the random variable of X.\n",
    "    c: float - Constant such that p(x) <= c * q(x) for all x.\n",
    "    sz: int - Number of random numbers to generate.\n",
    "\n",
    "    Returns:\n",
    "    list[int] - List of random numbers.\n",
    "    \"\"\"\n",
    "    def generate(H: callable, Hd: callable, p: callable, c: float) -> float:\n",
    "        while True:\n",
    "            U = rnd.random(); V = rnd.random()\n",
    "            HU = H(U); HdU = Hd(U)\n",
    "            if V < p(HU) * HdU / c: return HU\n",
    "    \n",
    "    return [generate(H, Hd, p, c) for _ in range(sz)]\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    # Check to generate Gamma(3/2, 1) with Y as exponential(2/3)\n",
    "    a = 3/2; b = 1\n",
    "    Y = lambda: exponential_distribution(2/3)[0]\n",
    "    p = lambda x : 2/np.pi * x**(1/2) * np.exp(-x)\n",
    "    q = lambda x : 2/3 * np.exp(-2/3 * x)\n",
    "\n",
    "    sz = 10**5\n",
    "    random_numbers = rejection_method(Y, p, q, 1.35, sz)\n",
    "    print(f\"Using Rejection Method:\")\n",
    "    print(f\"    Expected mean: {a * b} and variance: {a * b ** 2}\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "\n",
    "    # Check to generate Gamma(3/2, 1) with Y as exponential(2/3)\n",
    "    H = lambda x: -3/2 * np.log(1 - x)\n",
    "    Hd = lambda x: 3/2 / (1 - x)\n",
    "    c = 3 * np.sqrt(3/(2*np.pi*np.e))\n",
    "    random_numbers = transform_rejection_method(H, Hd, p, c, sz)\n",
    "    print(f\"Using Transform Rejection Method:\")\n",
    "    print(f\"    Expected mean: {a * b} and variance: {a * b ** 2}\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generación de VAs Normales"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Polar method:\n",
      "    Expected mean: -2 and variance: 1\n",
      "    Actual mean: -1.9975720415765061 and variance: 0.9944654824592785\n",
      "Using Box-Muller method:\n",
      "    Expected mean: -2 and variance: 1\n",
      "    Actual mean: -1.999559582657523 and variance: 1.0070003827111136\n",
      "Using Uniform Ratios method:\n",
      "    Expected mean: -2 and variance: 1\n",
      "    Actual mean: -1.999204512750367 and variance: 1.0045213088077496\n",
      "Using Rejection method:\n",
      "    Expected mean: -2 and variance: 1\n",
      "    Actual mean: -1.9983797147080524 and variance: 1.0011440391831785\n",
      "\n",
      "\n",
      "Using Polar method:\n",
      "    Expected mean: 2 and variance: 1\n",
      "    Actual mean: 1.9969144602373172 and variance: 1.0040767843622553\n",
      "Using Box-Muller method:\n",
      "    Expected mean: 2 and variance: 1\n",
      "    Actual mean: 1.9976467551279409 and variance: 0.9959351300310888\n",
      "Using Uniform Ratios method:\n",
      "    Expected mean: 2 and variance: 1\n",
      "    Actual mean: 2.0027375080040626 and variance: 0.9927588189486801\n",
      "Using Rejection method:\n",
      "    Expected mean: 2 and variance: 1\n",
      "    Actual mean: 1.9979867745591442 and variance: 0.9945239327689728\n",
      "\n",
      "\n",
      "Using Polar method:\n",
      "    Expected mean: 5 and variance: 4\n",
      "    Actual mean: 4.998113745783231 and variance: 3.9872093106662185\n",
      "Using Box-Muller method:\n",
      "    Expected mean: 5 and variance: 4\n",
      "    Actual mean: 4.999857386381171 and variance: 3.978575540579027\n",
      "Using Uniform Ratios method:\n",
      "    Expected mean: 5 and variance: 4\n",
      "    Actual mean: 4.993243663028752 and variance: 4.013701142899832\n",
      "Using Rejection method:\n",
      "    Expected mean: 5 and variance: 4\n",
      "    Actual mean: 5.002055262188756 and variance: 4.014365409134811\n",
      "\n",
      "\n",
      "Using Polar method:\n",
      "    Expected mean: 10 and variance: 9\n",
      "    Actual mean: 9.992287665998097 and variance: 8.963823888505912\n",
      "Using Box-Muller method:\n",
      "    Expected mean: 10 and variance: 9\n",
      "    Actual mean: 10.010332903524606 and variance: 8.928125881732475\n",
      "Using Uniform Ratios method:\n",
      "    Expected mean: 10 and variance: 9\n",
      "    Actual mean: 9.989898205840204 and variance: 8.991374869405004\n",
      "Using Rejection method:\n",
      "    Expected mean: 10 and variance: 9\n",
      "    Actual mean: 10.00686430445041 and variance: 8.994745967598055\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def normal_distribution(m: float, s: float, sz: int = 1, method: str = \"rejection\") -> list[float]:\n",
    "    \"\"\"\n",
    "    Generates random numbers from a normal distribution.\n",
    "\n",
    "    Parameters:\n",
    "    m: float\n",
    "        The mean of the normal distribution.\n",
    "    s: float\n",
    "        The standard deviation of the normal distribution.\n",
    "    sz: int\n",
    "        The number of random numbers to generate.\n",
    "    method: str\n",
    "        The method to use for generating random numbers. Can be \"rejection\", \"polar\", \"box-muller\" or \"uniform_ratios\".\n",
    "        Default is \"rejection\".\n",
    "\n",
    "    Returns:\n",
    "    list[float]\n",
    "        A list of random numbers from the normal distribution.\n",
    "    \"\"\"\n",
    "    def rejection_method() -> float:\n",
    "        while True:\n",
    "            u, y = -np.log(rnd.random()), -np.log(rnd.random())\n",
    "            if y >= (u - 1) ** 2 / 2: return (u if rnd.random() < 0.5 else -u)\n",
    "    \n",
    "    def polar_method() -> list[float]:\n",
    "        r2 = -2 * np.log(1 - rnd.random())\n",
    "        theta = 2 * np.pi * rnd.random()\n",
    "        x, y = np.sqrt(r2) * np.cos(theta), np.sqrt(r2) * np.sin(theta)\n",
    "        return [x, y]\n",
    "    \n",
    "    def box_muller_method() -> list[float]:\n",
    "        while True:\n",
    "            v1, v2 = 2 * rnd.random() - 1, 2 * rnd.random() - 1\n",
    "            if v1 ** 2 + v2 ** 2 <= 1:\n",
    "                s = v1 ** 2 + v2 ** 2\n",
    "                x, y = v1 * np.sqrt(-2 * np.log(s) / s), v2 * np.sqrt(-2 * np.log(s) / s)\n",
    "                return [x, y]\n",
    "        \n",
    "    def uniform_ratios_method() -> float:\n",
    "        c = 4 * np.exp(-0.5) / np.sqrt(2.0)\n",
    "        while True:\n",
    "            u, y = rnd.random(), 1 - rnd.random()\n",
    "            z = c * (u - 0.5) / y\n",
    "            if z ** 2 / 4 <= -np.log(y): return z\n",
    "    \n",
    "    match method:\n",
    "        case \"polar\":\n",
    "            r = []\n",
    "            while len(r) < sz: r += [m + x * s for x in polar_method()]\n",
    "            return r[:sz]\n",
    "        case \"box-muller\":\n",
    "            r = []\n",
    "            while len(r) < sz: r += [m + x * s for x in box_muller_method()]\n",
    "            return r[:sz]\n",
    "        case \"uniform_ratios\":\n",
    "            return [m + uniform_ratios_method() * s for _ in range(sz)]\n",
    "        case \"rejection\":\n",
    "            return [m + rejection_method() * s for _ in range(sz)]\n",
    "        case _:\n",
    "            raise ValueError(\"Invalid method. Please use 'rejection', 'polar', 'box-muller' or 'uniform_ratios'.\")\n",
    "    \n",
    "if __name__ == \"__main__\":\n",
    "    # Check if the generated random numbers are from the normal distribution.\n",
    "    m_list = [-2, 2, 5, 10]\n",
    "    s_list = [1, 1, 2, 3]\n",
    "    sz = 10**5\n",
    "\n",
    "    for i in range(len(m_list)):\n",
    "        m, s = m_list[i], s_list[i]\n",
    "\n",
    "        # Case 1: Using polar method.\n",
    "        random_numbers = normal_distribution(m, s, sz, \"polar\")\n",
    "        print(f\"Using Polar method:\")\n",
    "        print(f\"    Expected mean: {m} and variance: {s ** 2}\")\n",
    "        print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "\n",
    "        # Case 2: Using Box-Muller method.\n",
    "        random_numbers = normal_distribution(m, s, sz, \"box-muller\")\n",
    "        print(f\"Using Box-Muller method:\")\n",
    "        print(f\"    Expected mean: {m} and variance: {s ** 2}\")\n",
    "        print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "\n",
    "        # Case 3: Using Uniform Ratios method.\n",
    "        random_numbers = normal_distribution(m, s, sz, \"uniform_ratios\")\n",
    "        print(f\"Using Uniform Ratios method:\")\n",
    "        print(f\"    Expected mean: {m} and variance: {s ** 2}\")\n",
    "        print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "\n",
    "        # Case 4: Using Rejection method.\n",
    "        random_numbers = normal_distribution(m, s, sz, \"rejection\")\n",
    "        print(f\"Using Rejection method:\")\n",
    "        print(f\"    Expected mean: {m} and variance: {s ** 2}\")\n",
    "        print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "\n",
    "        print(\"\\n\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generación de Proceso de Poisson"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Homogéneo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected mean: 20\n",
      "Actual mean: 19.9129\n"
     ]
    }
   ],
   "source": [
    "def poisson_process_events(l: float, t: float) -> list[float]:\n",
    "    \"\"\"\n",
    "    Generates the events of a Poisson process until a given time 't'.\n",
    "\n",
    "    Parameters:\n",
    "    l: float\n",
    "        The rate parameter of the Poisson process.\n",
    "    t: float\n",
    "        The time until which the events are generated.\n",
    "\n",
    "    Returns:\n",
    "    list[float]\n",
    "        A list of times at which the events occur.\n",
    "    \"\"\"\n",
    "    x = 0; events = []\n",
    "    while True:\n",
    "        x += exponential_distribution(l)[0]\n",
    "        if x > t: break\n",
    "        events.append(x)\n",
    "    return events\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    # Check if the generated events are from a Poisson process.\n",
    "    l = 2\n",
    "    t = 10\n",
    "    sz = 10**4\n",
    "    cnt_events = [len(poisson_process_events(l, t)) for _ in range(sz)]\n",
    "    print(f\"Expected mean: {l * t}\")\n",
    "    print(f\"Actual mean: {np.mean(cnt_events)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### No homogéneo (*adelgazamiento*)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the basic method:\n",
      "    Expected mean: 21.834497011030297\n",
      "    Actual mean: 21.7811\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using the optimized method:\n",
      "    Expected mean: 21.834497011030297\n",
      "    Actual mean: 21.8463\n"
     ]
    }
   ],
   "source": [
    "def poisson_no_homogeneous_process_events(fl: callable, l: float, t: float) -> list[float]:\n",
    "    \"\"\"\n",
    "    Generates the events of a non-homogeneous Poisson process until a given time 't'.\n",
    "\n",
    "    Parameters:\n",
    "    fl: callable\n",
    "        The function that returns the rate parameter at time 't'.\n",
    "    l: float\n",
    "        The upper bound of the rate parameter.\n",
    "    t: float\n",
    "        The time until which the events are generated.\n",
    "\n",
    "    Returns:\n",
    "    list[float]\n",
    "        A list of times at which the events occur.\n",
    "    \"\"\"\n",
    "    x = 0; events = []\n",
    "    while True:\n",
    "        x += exponential_distribution(l)[0]\n",
    "        if x > t: break\n",
    "        if rnd.random() < fl(x) / l: events.append(x)\n",
    "    return events\n",
    "\n",
    "def poisson_no_homogeneous_process_events_optimized(fl: callable, l: list[float], t: list[float]) -> list[float]:\n",
    "    \"\"\"\n",
    "    Generates the events of a non-homogeneous Poisson process with time intervals until a given time 't[-1]'.\n",
    "\n",
    "    Parameters:\n",
    "    fl: callable\n",
    "        The function that returns the rate parameter at time 't'.\n",
    "    l: list[float]\n",
    "        The upper bound of the rate parameter.\n",
    "    t: list[float]\n",
    "        The time until which the events are generated (intervals).\n",
    "    \n",
    "    Returns:\n",
    "    list[float]\n",
    "        A list of times at which the events occur.\n",
    "    \"\"\"\n",
    "    x = 0; events = []; i = 0\n",
    "    while True:\n",
    "        x += exponential_distribution(l[i])[0]\n",
    "        while i != len(t) - 1 and x > t[i]: x = t[i] + (x - t[i]) * l[i] / l[i+1]; i += 1\n",
    "        if x > t[-1]: break\n",
    "        if rnd.random() < fl(x) / l[i]: events.append(x)\n",
    "    return events\n",
    "\n",
    "if __name__ == \"__main__\":\n",
    "    # Check if the generated events are from a non-homogeneous Poisson process.\n",
    "    fl = lambda x: 2 + np.sin(x)\n",
    "    l = 3\n",
    "    t = 10\n",
    "    sz = 10**4\n",
    "    cnt_events = [len(poisson_no_homogeneous_process_events(fl, l, t)) for _ in range(sz)]\n",
    "    print(f\"Using the basic method:\")\n",
    "    print(f\"    Expected mean: {t * np.mean([fl(x) for x in np.linspace(0, t, 1000)])}\")\n",
    "    print(f\"    Actual mean: {np.mean(cnt_events)}\")\n",
    "\n",
    "    l = [2 + np.sin(x) for x in np.linspace(0, 10, 1000)]\n",
    "    t = np.linspace(0, 10, 1000)\n",
    "    cnt_events = [len(poisson_no_homogeneous_process_events_optimized(fl, l, t)) for _ in range(sz)]\n",
    "    print(f\"Using the optimized method:\")\n",
    "    print(f\"    Expected mean: {t[-1] * np.mean([fl(x) for x in np.linspace(0, t[-1], 1000)])}\")\n",
    "    print(f\"    Actual mean: {np.mean(cnt_events)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Método de Composición"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def composition_method(p: list[float], f: list[callable], sz: int = 1) -> list[float]:\n",
    "    \"\"\"\n",
    "    Generates random numbers from a distribution using the composition method.\n",
    "\n",
    "    Parameters:\n",
    "    p: list[float]\n",
    "        The probabilities of the distributions.\n",
    "    f: list[callable]\n",
    "        The functions that generate random numbers from the distributions.\n",
    "    sz: int\n",
    "        The number of random numbers to generate.\n",
    "\n",
    "    Returns:\n",
    "    list[float]\n",
    "        A list of random numbers from the distribution.\n",
    "    \"\"\"\n",
    "    def generate(p: list[float], f: list[callable]) -> float:\n",
    "        U = rnd.random()\n",
    "        i = 0\n",
    "        while U > p[i]: U -= p[i]; i += 1\n",
    "        return f[i]()\n",
    "    \n",
    "    return [generate(p, f) for _ in range(sz)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "c:\\Users\\emanu\\anaconda3\\envs\\famaf-mys\\Lib\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
      "  with pd.option_context('mode.use_inf_as_na', True):\n",
      "c:\\Users\\emanu\\anaconda3\\envs\\famaf-mys\\Lib\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
      "  with pd.option_context('mode.use_inf_as_na', True):\n",
      "c:\\Users\\emanu\\anaconda3\\envs\\famaf-mys\\Lib\\site-packages\\seaborn\\_oldcore.py:1119: FutureWarning: use_inf_as_na option is deprecated and will be removed in a future version. Convert inf values to NaN before operating instead.\n",
      "  with pd.option_context('mode.use_inf_as_na', True):\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x1500 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Item A\n",
    "def ej1_fa_density(x):\n",
    "    if 2 <= x <= 3:\n",
    "        return (x - 2) / 2\n",
    "    elif 3 <= x <= 6:\n",
    "        return (2 - x/3) / 2\n",
    "    return 0\n",
    "\n",
    "def ej1_fa_inverse(p):\n",
    "    assert 0 <= p <= 1, \"p must be in [0, 1]\"\n",
    "    if 0 <= p <= 1/4:\n",
    "        return 2 * (1 + np.sqrt(p))\n",
    "    elif 1/4 <= p <= 1:\n",
    "        return 6 * (1 - np.sqrt((1 - p) / 3))\n",
    "    \n",
    "# Item B\n",
    "def ej1_fb_density(x):\n",
    "    if 0 <= x <= 1:\n",
    "        return 6 * (x + 3) / 35\n",
    "    elif 1 <= x <= 2:\n",
    "        return 6 * x**2 / 35\n",
    "    return 0\n",
    "\n",
    "def ej1_fb_inverse(p):\n",
    "    assert 0 <= p <= 1, \"p must be in [0, 1]\"\n",
    "    if 0 <= p <= 3/5:\n",
    "        return -3 + np.sqrt(9 + 35 * p / 3)\n",
    "    elif 3/5 <= p <= 1:\n",
    "        return np.cbrt((35 * p - 19) / 2)\n",
    "\n",
    "# Item C\n",
    "def ej1_fc_density(x):\n",
    "    if x <= 0:\n",
    "        return np.exp(4 * x) / 4\n",
    "    elif 0 <= x <= 15/4:\n",
    "        return 1/4\n",
    "    return 0\n",
    "\n",
    "def ej1_fc_inverse(p):\n",
    "    assert 0 < p <= 1, \"p must be in (0, 1]\"\n",
    "    if 0 < p <= 1/16:\n",
    "        return np.log(16 * p) / 4\n",
    "    elif 1/16 <= p <= 1:\n",
    "        return (16 * p - 1) / 4\n",
    "\n",
    "# Generate all variables\n",
    "sz = 10**5\n",
    "random_numbers_a = [inverse_transform_method(ej1_fa_inverse) for _ in range(sz)]\n",
    "random_numbers_b = [inverse_transform_method(ej1_fb_inverse) for _ in range(sz)]\n",
    "random_numbers_c = [inverse_transform_method(ej1_fc_inverse) for _ in range(sz)]\n",
    "\n",
    "# Check if the generated random numbers are from the given distributions.\n",
    "# Graphic representation of the generated random numbers vs the corresponding density function (one above the other).\n",
    "# Use kdeplot to estimate the density function of the generated random numbers.\n",
    "\n",
    "fig, axs = plt.subplots(2, 2, figsize=(15, 15))\n",
    "\n",
    "# Item A\n",
    "sns.kdeplot(random_numbers_a, ax=axs[0, 0])\n",
    "x = np.linspace(2, 6, 10000)\n",
    "y = [ej1_fa_density(i) for i in x]\n",
    "axs[0, 0].plot(x, y, color='red')\n",
    "axs[0, 0].set_title(\"Item A\")\n",
    "axs[0, 0].legend([\"Random numbers\", \"Density function\"])\n",
    "\n",
    "# Item B\n",
    "sns.kdeplot(random_numbers_b, ax=axs[0, 1])\n",
    "x = np.linspace(0, 2, 10000)\n",
    "y = [ej1_fb_density(i) for i in x]\n",
    "axs[0, 1].plot(x, y, color='red')\n",
    "axs[0, 1].set_title(\"Item B\")\n",
    "axs[0, 1].legend([\"Random numbers\", \"Density function\"])\n",
    "\n",
    "# Item C\n",
    "sns.kdeplot(random_numbers_c, ax=axs[1, 0])\n",
    "x = np.linspace(-1, 15/4, 10000)\n",
    "y = [ej1_fc_density(i) for i in x]\n",
    "axs[1, 0].plot(x, y, color='red')\n",
    "axs[1, 0].set_title(\"Item C\")\n",
    "axs[1, 0].legend([\"Random numbers\", \"Density function\"])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Pareto(2)\n",
      "    Expected mean: 2.0\n",
      "    Actual mean: 2.0129023640718775\n",
      "Erlang(2, 2)\n",
      "    Expected mean: 4\n",
      "    Actual mean: 3.998511086981939\n",
      "Weibull(1, 2)\n",
      "    Expected mean: 0.8862269254527579\n",
      "    Actual mean: 0.8845603666541298\n"
     ]
    }
   ],
   "source": [
    "# Pareto\n",
    "def ej2_pareto_inverse(p, a):\n",
    "    assert 0 < p < 1 and 0 < a, \"Invalid values for p and a\"\n",
    "    return (1 / (1 - p)) ** (1 / a)\n",
    "\n",
    "def ej2_pareto(a):\n",
    "    sz = 10**5\n",
    "    random_numbers = [ej2_pareto_inverse(rnd.random(), a) for _ in range(sz)]\n",
    "\n",
    "    expected_value = a / (a - 1)\n",
    "    print(f\"Pareto({a})\")\n",
    "    print(f\"    Expected mean: {expected_value}\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "\n",
    "# Erlang\n",
    "def ej2_erlang(k, m):\n",
    "    sz = 10**5\n",
    "    random_numbers = gamma_distribution(k, m, sz)\n",
    "\n",
    "    expected_value = k * m\n",
    "    print(f\"Erlang({k}, {m})\")\n",
    "    print(f\"    Expected mean: {expected_value}\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "\n",
    "# Weibull\n",
    "def ej2_weibull_inverse(p, l, b):\n",
    "    assert 0 < p < 1 and 0 < l and 0 < b, \"Invalid values for p, l and b\"\n",
    "    return l * (-np.log(1 - p)) ** (1 / b)\n",
    "\n",
    "def ej2_weibull(l, b):\n",
    "    sz = 10**5\n",
    "    random_numbers = [ej2_weibull_inverse(rnd.random(), l, b) for _ in range(sz)]\n",
    "\n",
    "    expected_value = l / b * math.gamma(1 / b)\n",
    "    print(f\"Weibull({l}, {b})\")\n",
    "    print(f\"    Expected mean: {expected_value}\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "\n",
    "# Check if the generated random numbers are from the given distributions.\n",
    "ej2_pareto(2)\n",
    "ej2_erlang(2, 2)\n",
    "ej2_weibull(1, 2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Expected mean: 4.4\n",
      "Actual mean: 4.394706548842697\n"
     ]
    }
   ],
   "source": [
    "f1 = lambda: exponential_distribution(1/3)[0]\n",
    "f2 = lambda: exponential_distribution(1/5)[0]\n",
    "f3 = lambda: exponential_distribution(1/7)[0]\n",
    "f = [f1, f2, f3]; p = [0.5, 0.3, 0.2]\n",
    "sz = 10**5\n",
    "random_numbers = composition_method(p, f, sz)\n",
    "print(f\"Expected mean: {3 * 0.5 + 5 * 0.3 + 7 * 0.2}\")\n",
    "print(f\"Actual mean: {np.mean(random_numbers)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual mean: 0.40563770508297625\n"
     ]
    }
   ],
   "source": [
    "def ej4_generate():\n",
    "    y = exponential_distribution(1)[0]\n",
    "    u = rnd.random()\n",
    "    return u ** (1 / y)\n",
    "\n",
    "sz = 10**5\n",
    "random_numbers = [ej4_generate() for _ in range(sz)]\n",
    "print(f\"Actual mean: {np.mean(random_numbers)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The samples are:\n",
      "    M: [1.6439806748561103, 0.5401096760906309, 1.0446137365762231, 0.693392573604811, 2.4424754834585003, 0.7248650860728155, 0.2353157473188414, 0.5222086731157571, 1.2023650066637885, 1.4031648958091136]\n",
      "    m: [0.43056068534964126, 0.025901726172558814, 0.1638433273972819, 0.07672814715029312, 0.05973482352553972, 0.02881937638990219, 0.03250986115226296, 0.276273505195122, 0.075996462074117, 0.31452794769771175]\n",
      "The means of bigger samples (10^5) are:\n",
      "    M: 1.215545810425765\n",
      "    m: 0.16614322023441316\n"
     ]
    }
   ],
   "source": [
    "def ej5_generate(l_list):\n",
    "    x = [exponential_distribution(l)[0] for l in l_list]\n",
    "    return max(x), min(x)\n",
    "\n",
    "sz = 10\n",
    "l_list = [1, 2, 3]\n",
    "random_numbers = [ej5_generate(l_list) for _ in range(sz)]\n",
    "M, m = [x[0] for x in random_numbers], [x[1] for x in random_numbers]\n",
    "print(f\"The samples are:\")\n",
    "print(f\"    M: {M}\")\n",
    "print(f\"    m: {m}\")\n",
    "\n",
    "sz = 10**5\n",
    "random_numbers = [ej5_generate(l_list) for _ in range(sz)]\n",
    "M, m = [x[0] for x in random_numbers], [x[1] for x in random_numbers]\n",
    "print(f\"The means of bigger samples (10^5) are:\")\n",
    "print(f\"    M: {np.mean(M)}\")\n",
    "print(f\"    m: {np.mean(m)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 2\n",
      "    Rejection Method:\n",
      "        Actual mean: 0.6684458435587926\n",
      "        Time: 0.013999223709106445\n",
      "    Inverse Transform Method:\n",
      "        Actual mean: 0.6635064004181985\n",
      "        Time: 0.0019998550415039062\n",
      "    Uniform Max Method:\n",
      "        Actual mean: 0.6630702928927884\n",
      "        Time: 0.006000518798828125\n",
      "n = 3\n",
      "    Rejection Method:\n",
      "        Actual mean: 0.7508218737297632\n",
      "        Time: 0.012001276016235352\n",
      "    Inverse Transform Method:\n",
      "        Actual mean: 0.7490253789040352\n",
      "        Time: 0.0029985904693603516\n",
      "    Uniform Max Method:\n",
      "        Actual mean: 0.7499812516052251\n",
      "        Time: 0.006000041961669922\n",
      "n = 50\n",
      "    Rejection Method:\n",
      "        Actual mean: 0.9801922691429842\n",
      "        Time: 0.17799997329711914\n",
      "    Inverse Transform Method:\n",
      "        Actual mean: 0.98099255748876\n",
      "        Time: 0.002000570297241211\n",
      "    Uniform Max Method:\n",
      "        Actual mean: 0.9806621775206235\n",
      "        Time: 0.03599977493286133\n",
      "n = 100\n",
      "    Rejection Method:\n",
      "        Actual mean: 0.9901741741821175\n",
      "        Time: 0.442000150680542\n",
      "    Inverse Transform Method:\n",
      "        Actual mean: 0.9900559955790459\n",
      "        Time: 0.0019996166229248047\n",
      "    Uniform Max Method:\n",
      "        Actual mean: 0.990126245319309\n",
      "        Time: 0.0670006275177002\n"
     ]
    }
   ],
   "source": [
    "def ej6_rejection_method(n, sz):\n",
    "    Y = lambda: rnd.random()\n",
    "    p = lambda x: n * x ** (n - 1)\n",
    "    q = lambda y: 1\n",
    "    c = n\n",
    "\n",
    "    return rejection_method(Y, p, q, c, sz)\n",
    "\n",
    "def ej6_inverse_transform_method(n, sz):\n",
    "    def generate(n):\n",
    "        u = rnd.random()\n",
    "        return u ** (1 / n)\n",
    "    \n",
    "    return [generate(n) for _ in range(sz)]\n",
    "\n",
    "def ej6_uniform_max_method(n, sz):\n",
    "    def generate(n):\n",
    "        u = [rnd.random() for _ in range(n)]\n",
    "        return max(u)\n",
    "    \n",
    "    return [generate(n) for _ in range(sz)]\n",
    "\n",
    "# Compare the three methods for n = 2, 3, 50, 100 and sz = 10^4.\n",
    "n_list = [2, 3, 50, 100]\n",
    "sz = 10**4\n",
    "\n",
    "for n in n_list:\n",
    "    print(f\"n = {n}\")\n",
    "    print(f\"    Rejection Method:\")\n",
    "    act_time = time()\n",
    "    random_numbers = ej6_rejection_method(n, sz)\n",
    "    act_time = time() - act_time\n",
    "    print(f\"        Actual mean: {np.mean(random_numbers)}\")\n",
    "    print(f\"        Time: {act_time}\")\n",
    "\n",
    "    print(f\"    Inverse Transform Method:\")\n",
    "    act_time = time()\n",
    "    random_numbers = ej6_inverse_transform_method(n, sz)\n",
    "    act_time = time() - act_time\n",
    "    print(f\"        Actual mean: {np.mean(random_numbers)}\")\n",
    "    print(f\"        Time: {act_time}\")\n",
    "\n",
    "    print(f\"    Uniform Max Method:\")\n",
    "    act_time = time()\n",
    "    random_numbers = ej6_uniform_max_method(n, sz)\n",
    "    act_time = time() - act_time\n",
    "    print(f\"        Actual mean: {np.mean(random_numbers)}\")\n",
    "    print(f\"        Time: {act_time}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 7"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ITEM B\n",
      "Inverse Transform Method:\n",
      "    Actual mean: 1.7164774570894914\n",
      "    Time: 0.10299992561340332\n",
      "Rejection Method:\n",
      "    Actual mean: 1.716142140314704\n",
      "    Time: 0.08800005912780762\n",
      "ITEM C -> The real P(X <= 2) is 0.6931471805599453\n",
      "Inverse Transform Method:\n",
      "    P(X <= 2): 0.69465\n",
      "Rejection Method:\n",
      "    P(X <= 2): 0.69192\n"
     ]
    }
   ],
   "source": [
    "def ej7_inverse_transform_method(sz):\n",
    "    f_inv = lambda p: np.exp(p)\n",
    "    return [inverse_transform_method(f_inv) for _ in range(sz)]\n",
    "\n",
    "def ej7_rejection_method(sz):\n",
    "    Y = lambda: rnd.random() * (np.e - 1) + 1\n",
    "    p = lambda x: 1 / x\n",
    "    q = lambda x: 1 / np.e\n",
    "    c = np.e\n",
    "\n",
    "    return rejection_method(Y, p, q, c, sz)\n",
    "\n",
    "def ej7_itemB():\n",
    "    # Compare the two methods for sz = 10^4.\n",
    "    sz = 10**5\n",
    "\n",
    "    print(f\"ITEM B\")\n",
    "    print(\"Inverse Transform Method:\")\n",
    "    act_time = time()\n",
    "    random_numbers = ej7_inverse_transform_method(sz)\n",
    "    act_time = time() - act_time\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "    print(f\"    Time: {act_time}\")\n",
    "\n",
    "    print(\"Rejection Method:\")\n",
    "    act_time = time()\n",
    "    random_numbers = ej7_rejection_method(sz)\n",
    "    act_time = time() - act_time\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "    print(f\"    Time: {act_time}\")\n",
    "\n",
    "def ej7_itemC():\n",
    "    # Calculate P(X <= 2) with the two methods.\n",
    "    sz = 10**5\n",
    "\n",
    "    print(f\"ITEM C -> The real P(X <= 2) is {np.log(2)}\")\n",
    "    print(\"Inverse Transform Method:\")\n",
    "    random_numbers = ej7_inverse_transform_method(sz)\n",
    "    p = len([x for x in random_numbers if x <= 2]) / sz\n",
    "    print(f\"    P(X <= 2): {p}\")\n",
    "\n",
    "    print(\"Rejection Method:\")\n",
    "    random_numbers = ej7_rejection_method(sz)\n",
    "    p = len([x for x in random_numbers if x <= 2]) / sz\n",
    "    print(f\"    P(X <= 2): {p}\")\n",
    "\n",
    "ej7_itemB()\n",
    "ej7_itemC()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "MEAN COMPARISON\n",
      "Uniform Sum Method:\n",
      "    Actual mean: 0.9984801824569683\n",
      "Inverse Transform Method:\n",
      "    Actual mean: 0.9984915181817383\n",
      "Rejection Method:\n",
      "    Actual mean: 1.0005057856666606\n",
      "\n",
      "PROBABILITY COMPARISON of P(X > x_0) = 0.125\n",
      "Uniform Sum Method:\n",
      "    x0: 1.0008907664987985\n",
      "Inverse Transform Method:\n",
      "    x0: 1.0010092666798307\n",
      "Rejection Method:\n",
      "    x0: 0.9944406922218311\n"
     ]
    }
   ],
   "source": [
    "def ej8_uniform_sum_method(sz):\n",
    "    def generate():\n",
    "        u = [rnd.random() for _ in range(2)]\n",
    "        return sum(u)\n",
    "    \n",
    "    return [generate() for _ in range(sz)]\n",
    "\n",
    "def ej8_inverse_transform_method(sz):\n",
    "    def f_inv(p):\n",
    "        assert 0 <= p <= 1, \"p must be in [0, 1]\"\n",
    "        if 0 <= p <= 1/2:\n",
    "            return np.sqrt(2 * p)\n",
    "        elif 1/2 <= p <= 1:\n",
    "            return 2 - np.sqrt(2 * (1 - p))\n",
    "    \n",
    "    return [inverse_transform_method(f_inv) for _ in range(sz)]\n",
    "\n",
    "def ej8_rejection_method(sz):\n",
    "    Y = lambda: rnd.random() * 2\n",
    "    p = lambda x: x if 0 <= x <= 1 else (2 - x if 1 <= x <= 2 else 0)\n",
    "    q = lambda x: 1 / 2\n",
    "    c = 2\n",
    "\n",
    "    return rejection_method(Y, p, q, c, sz)\n",
    "\n",
    "def ej8_x0_prob(vals, p_lim):\n",
    "    p = 1; i = 0; sz = len(vals)\n",
    "    for x in sorted(vals):\n",
    "        if p < p_lim: return vals[i - 1]\n",
    "        sz -= 1; p = sz / len(vals); i += 1\n",
    "    return vals[-1]\n",
    "\n",
    "def ej8_mean_comparison():\n",
    "    sz = 10**5\n",
    "\n",
    "    print(f\"MEAN COMPARISON\")\n",
    "    print(\"Uniform Sum Method:\")\n",
    "    random_numbers = ej8_uniform_sum_method(sz)\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "\n",
    "    print(\"Inverse Transform Method:\")\n",
    "    random_numbers = ej8_inverse_transform_method(sz)\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "\n",
    "    print(\"Rejection Method:\")\n",
    "    random_numbers = ej8_rejection_method(sz)\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)}\")\n",
    "    print()\n",
    "\n",
    "def ej8_x0_prob_comparison():\n",
    "    print(f\"PROBABILITY COMPARISON of P(X > x_0) = 0.125\")\n",
    "    sz = 10**3; sz2 = 10**3\n",
    "    print(\"Uniform Sum Method:\")\n",
    "    x0 = [ej8_x0_prob(ej8_uniform_sum_method(sz), 0.125) for _ in range(sz2)]\n",
    "    print(f\"    x0: {np.mean(x0)}\")\n",
    "\n",
    "    print(\"Inverse Transform Method:\")\n",
    "    x0 = [ej8_x0_prob(ej8_inverse_transform_method(sz), 0.125) for _ in range(sz2)]\n",
    "    print(f\"    x0: {np.mean(x0)}\")\n",
    "\n",
    "    print(\"Rejection Method:\")\n",
    "    x0 = [ej8_x0_prob(ej8_rejection_method(sz), 0.125) for _ in range(sz2)]\n",
    "    print(f\"    x0: {np.mean(x0)}\")\n",
    "\n",
    "ej8_mean_comparison()\n",
    "ej8_x0_prob_comparison()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Using Rejection method:\n",
      "    Actual mean: 99.99527288297351 and variance: 8.959684578234418\n",
      "    Time: 0.38700032234191895\n",
      "Using Polar method:\n",
      "    Actual mean: 99.98344367830286 and variance: 8.961572213524386\n",
      "    Time: 0.23099851608276367\n",
      "Using Uniform Ratios method:\n",
      "    Actual mean: 99.98330798657767 and variance: 9.031594698596573\n",
      "    Time: 0.38899755477905273\n"
     ]
    }
   ],
   "source": [
    "# Compare the three methods for sz = 10^5.\n",
    "sz = 10**5\n",
    "m = 100; s = 3\n",
    "print(f\"Using Rejection method:\")\n",
    "act_time = time()\n",
    "random_numbers = normal_distribution(m, s, sz, \"rejection\")\n",
    "act_time = time() - act_time\n",
    "print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "print(f\"    Time: {act_time}\")\n",
    "\n",
    "print(f\"Using Polar method:\")\n",
    "act_time = time()\n",
    "random_numbers = normal_distribution(m, s, sz, \"polar\")\n",
    "act_time = time() - act_time\n",
    "print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "print(f\"    Time: {act_time}\")\n",
    "\n",
    "print(f\"Using Uniform Ratios method:\")\n",
    "act_time = time()\n",
    "random_numbers = normal_distribution(m, s, sz, \"uniform_ratios\")\n",
    "act_time = time() - act_time\n",
    "print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "print(f\"    Time: {act_time}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 11"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cauchy(1)\n",
      "    Actual mean: 1.1105181691327615 and variance: 5727.226207198371\n",
      "    Proportion of values in [-l, l]: 0.5047 vs. real value: 0.5\n",
      "    Time: 0.007997751235961914\n",
      "Cauchy(2.5)\n",
      "    Actual mean: -0.2150487091601447 and variance: 18516.617058004118\n",
      "    Proportion of values in [-l, l]: 0.5049 vs. real value: 0.5\n",
      "    Time: 0.013000011444091797\n",
      "Cauchy(0.3)\n",
      "    Actual mean: -0.4932563196692502 and variance: 1101.6741493712\n",
      "    Proportion of values in [-l, l]: 0.5027 vs. real value: 0.5\n",
      "    Time: 0.006999969482421875\n"
     ]
    }
   ],
   "source": [
    "def ej11_cauchy_standardized_distribution(sz):\n",
    "    def generate():\n",
    "        while True:\n",
    "            u, v = rnd.random() * 2 - 1, rnd.random() * 2 - 1\n",
    "            if v**2 + u**2 <= 1:\n",
    "                return v / u\n",
    "    \n",
    "    return [generate() for _ in range(sz)]\n",
    "\n",
    "\n",
    "def ej11_cauchy_distribution(l, sz):\n",
    "    return [l * x for x in ej11_cauchy_standardized_distribution(sz)]\n",
    "\n",
    "sz = 10**4\n",
    "l_list = [1, 2.5, 0.3]\n",
    "\n",
    "for l in l_list:\n",
    "    act_time = time()\n",
    "    random_numbers = ej11_cauchy_distribution(l, sz)\n",
    "    act_time = time() - act_time\n",
    "    proportion = len([x for x in random_numbers if -l <= x <= l]) / sz\n",
    "    print(f\"Cauchy({l})\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "    print(f\"    Proportion of values in [-l, l]: {proportion} vs. real value: {1/2}\")\n",
    "    print(f\"    Time: {act_time}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 12"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cauchy(1) with Inverse Transform Method\n",
      "    Actual mean: 0.12182083097036579 and variance: 1022.9489632617413\n",
      "    Proportion of values in [-l, l]: 0.4976 vs. real value: 0.5\n",
      "    Time: 0.010999679565429688\n",
      "0.9973557010035816\n",
      "Cauchy(1) with Rejection Method for Normal(0, 1.25) ==> No tiene sentido dada que las cotas (c) no son las correctas nunca\n",
      "    Actual mean: -0.010854516831312604 and variance: 1.5580482958341424\n",
      "    Proportion of values in [-l, l]: 0.6247 vs. real value: 0.5\n",
      "    Time: 0.0879971981048584\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cauchy(2.5) with Inverse Transform Method\n",
      "    Actual mean: 0.9667698857732827 and variance: 116512.25107268385\n",
      "    Proportion of values in [-l, l]: 0.4956 vs. real value: 0.5\n",
      "    Time: 0.018999814987182617\n",
      "0.989376855395553\n",
      "Cauchy(2.5) with Rejection Method for Normal(0, 3.1) ==> No tiene sentido dada que las cotas (c) no son las correctas nunca\n",
      "    Actual mean: 0.005763436788395348 and variance: 9.44061199312358\n",
      "    Proportion of values in [-l, l]: 0.6275 vs. real value: 0.5\n",
      "    Time: 0.08700013160705566\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1500x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cauchy(0.3) with Inverse Transform Method\n",
      "    Actual mean: 0.4473487494199867 and variance: 835.1837221448435\n",
      "    Proportion of values in [-l, l]: 0.5009 vs. real value: 0.5\n",
      "    Time: 0.023999691009521484\n",
      "0.9308653209366761\n",
      "Cauchy(0.3) with Rejection Method for Normal(0, 0.35) ==> No tiene sentido dada que las cotas (c) no son las correctas nunca\n",
      "    Actual mean: 0.00031620547915078666 and variance: 0.1228535150158521\n",
      "    Proportion of values in [-l, l]: 0.6329 vs. real value: 0.5\n",
      "    Time: 0.17799973487854004\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def ej12_cauchy_density(x, l):\n",
    "    return l/np.pi * 1/(l**2 + x**2)\n",
    "\n",
    "def ej12_cauchy_cumulative(x, l):\n",
    "    return 1/2 + np.arctan(x/l) / np.pi\n",
    "\n",
    "def ej12_cauchy_inverse_cumulative(p):\n",
    "    assert 0 <= p <= 1, \"p must be in [0, 1]\"\n",
    "    return l * np.tan(np.pi * (p - 1/2))\n",
    "\n",
    "def ej12_cauchy_inverse_transform_method(l):\n",
    "    return [inverse_transform_method(ej12_cauchy_inverse_cumulative) for _ in range(sz)]\n",
    "\n",
    "def ej12_cauchy_rejection_method(l, s):\n",
    "    Y = lambda: normal_distribution(0, s)[0]\n",
    "    p = lambda x: ej12_cauchy_density(x, l)\n",
    "    q = lambda x: 1/(s * np.sqrt(2*np.pi)) * np.exp(-x**2/(2*s**2))\n",
    "    c = p(0)/q(0); print(c)\n",
    "\n",
    "    return rejection_method(Y, p, q, c, sz)\n",
    "\n",
    "def ej12_graphical_representation(l, m, s):\n",
    "    # Graphic a cauchy distribution and a normal one, one above the other.\n",
    "    x = np.linspace(-10, 10, 1000)\n",
    "    y = [ej12_cauchy_density(i, l) for i in x]\n",
    "    y2 = [st.norm.pdf(i, m, s) for i in x]\n",
    "\n",
    "    plt.figure(figsize=(15, 5))\n",
    "    plt.plot(x, y, color='red')\n",
    "    plt.plot(x, y2, color='blue')\n",
    "    plt.title(\"Cauchy vs Normal distribution\")\n",
    "    plt.legend([\"Cauchy\", \"Normal\"])\n",
    "    plt.show()\n",
    "\n",
    "sz = 10**4\n",
    "l_list = [1, 2.5, 0.3]\n",
    "s_list = [1.25, 3.1, 0.35]\n",
    "\n",
    "for i in range(len(l_list)):\n",
    "    l = l_list[i]; s = s_list[i]\n",
    "    ej12_graphical_representation(l, 0, s)\n",
    "\n",
    "    act_time = time()\n",
    "    random_numbers = ej12_cauchy_inverse_transform_method(l)\n",
    "    act_time = time() - act_time\n",
    "    proportion = len([x for x in random_numbers if -l <= x <= l]) / sz\n",
    "    print(f\"Cauchy({l}) with Inverse Transform Method\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "    print(f\"    Proportion of values in [-l, l]: {proportion} vs. real value: {1/2}\")\n",
    "    print(f\"    Time: {act_time}\")\n",
    "\n",
    "    act_time = time()\n",
    "    random_numbers = ej12_cauchy_rejection_method(l, s)\n",
    "    act_time = time() - act_time\n",
    "    proportion = len([x for x in random_numbers if -l <= x <= l]) / sz\n",
    "    print(f\"Cauchy({l}) with Rejection Method for Normal(0, {s}) ==> No tiene sentido dada que las cotas (c) no son las correctas nunca\")\n",
    "    print(f\"    Actual mean: {np.mean(random_numbers)} and variance: {np.var(random_numbers)}\")\n",
    "    print(f\"    Proportion of values in [-l, l]: {proportion} vs. real value: {1/2}\")\n",
    "    print(f\"    Time: {act_time}\")\n",
    "    print()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 14"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual mean: 149.6239\n"
     ]
    }
   ],
   "source": [
    "def ej14_simulate(l, t, tam):\n",
    "    events = poisson_process_events(l, t)\n",
    "    r = 0\n",
    "    for _ in range(len(events)): r += tam[rnd.randint(0, len(tam) - 1)]\n",
    "    return r\n",
    "\n",
    "sz = 10**5\n",
    "l = 5; t = 1; tam = [i for i in range(20, 41)]\n",
    "random_numbers = [ej14_simulate(l, t, tam) for _ in range(sz)]\n",
    "print(f\"Actual mean: {np.mean(random_numbers)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Ejercicio 15"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1500x500 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ITEM A: Common method\n",
      "Function (i): 3 + 4/(x + 1) with x into [0, 3]\n",
      "    Actual mean: 14.6026\n",
      "Function (ii): (x - 2) ** 2 - 5 * x + 17 with x into [0, 5]\n",
      "    Actual mean: 34.0979\n",
      "Function (iii): x/2-1 if 2 <= x <= 3 else 1-x/6 with x into [2, 6]\n",
      "    Actual mean: 0.6717\n",
      "\n",
      "ITEM B: Optimized method\n",
      "Function (i): 3 + 4/(x + 1) with x into [0, 3] and with intervals [0, 1/2, 1, 2, 3]\n",
      "    Actual mean: 14.5523\n",
      "Function (ii): (x - 2) ** 2 - 5 * x + 17 with x into [0, 5] and with intervals [0, 1, 2, 3, 5]\n",
      "    Actual mean: 34.1678\n",
      "Function (iii): x/2-1 if 2 <= x <= 3 else 1-x/6 with x into [2, 6] and with intervals [2+1/3, 2+2/3, 3, 3+1/3, 3+2/3, 4, 4+1/3, 4+2/3, 5, 5+1/3, 5+2/3, 6]\n",
      "    Actual mean: 1.0013\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def f1(x): \n",
    "    if 0 <= x <= 3: return 3 + 4/(x + 1)\n",
    "    return 0\n",
    "\n",
    "def f2(x):\n",
    "    if 0 <= x <= 5: return (x - 2) ** 2 - 5 * x + 17\n",
    "    return 0\n",
    "\n",
    "def f3(x):\n",
    "    if 2 <= x <= 3: return x/2 - 1\n",
    "    elif 3 < x <= 6: return 1 - x/6\n",
    "    return 0\n",
    "\n",
    "def ej15_graphic_representation():\n",
    "    fig, axs = plt.subplots(1, 3, figsize=(15, 5))\n",
    "\n",
    "    x = np.linspace(0, 3, 1000)\n",
    "    y = [f1(i) for i in x]\n",
    "    axs[0].plot(x, y)\n",
    "    axs[0].set_title(\"Function (i)\")\n",
    "    axs[0].set_xlabel(\"x\")\n",
    "    axs[0].set_ylabel(\"f(x)\")\n",
    "\n",
    "    x = np.linspace(0, 5, 1000)\n",
    "    y = [f2(i) for i in x]\n",
    "    axs[1].plot(x, y)\n",
    "    axs[1].set_title(\"Function (ii)\")\n",
    "    axs[1].set_xlabel(\"x\")\n",
    "    axs[1].set_ylabel(\"f(x)\")\n",
    "\n",
    "    x = np.linspace(0, 6, 1000)\n",
    "    y = [f3(i) for i in x]\n",
    "    axs[2].plot(x, y)\n",
    "    axs[2].set_title(\"Function (iii)\")\n",
    "    axs[2].set_xlabel(\"x\")\n",
    "    axs[2].set_ylabel(\"f(x)\")\n",
    "\n",
    "    plt.show()\n",
    "\n",
    "# Item A:\n",
    "def ej15_itemA():\n",
    "    sz = 10**4\n",
    "\n",
    "    print(f\"ITEM A: Common method\")\n",
    "    print(f\"Function (i): 3 + 4/(x + 1) with x into [0, 3]\")\n",
    "    l = 7; t = 3\n",
    "    mean = np.mean([len(poisson_no_homogeneous_process_events(f1, l, t)) for _ in range(sz)])\n",
    "    print(f\"    Actual mean: {mean}\")\n",
    "\n",
    "    print(f\"Function (ii): (x - 2) ** 2 - 5 * x + 17 with x into [0, 5]\")\n",
    "    l = 21; t = 5\n",
    "    mean = np.mean([len(poisson_no_homogeneous_process_events(f2, l, t)) for _ in range(sz)])\n",
    "    print(f\"    Actual mean: {mean}\")\n",
    "\n",
    "    print(f\"Function (iii): x/2-1 if 2 <= x <= 3 else 1-x/6 with x into [2, 6]\")\n",
    "    l = 1/2; t = 4\n",
    "    mean = np.mean([len(poisson_no_homogeneous_process_events(f3, l, t)) for _ in range(sz)])\n",
    "    print(f\"    Actual mean: {mean}\")\n",
    "    print()\n",
    "\n",
    "def ej15_itemB():\n",
    "    sz = 10**4\n",
    "\n",
    "    print(f\"ITEM B: Optimized method\")\n",
    "    print(f\"Function (i): 3 + 4/(x + 1) with x into [0, 3] and with intervals [0, 1/2, 1, 2, 3]\")\n",
    "    t = [1/2, 1, 2, 3]\n",
    "    l = [f1(0), f1(1/2), f1(1), f1(2)]\n",
    "    mean = np.mean([len(poisson_no_homogeneous_process_events_optimized(f1, l, t)) for _ in range(sz)])\n",
    "    print(f\"    Actual mean: {mean}\")\n",
    "\n",
    "    print(f\"Function (ii): (x - 2) ** 2 - 5 * x + 17 with x into [0, 5] and with intervals [0, 1, 2, 3, 5]\")\n",
    "    t = [1, 2, 3, 5]\n",
    "    l = [f2(0), f2(1), f2(2), f2(3)]\n",
    "    mean = np.mean([len(poisson_no_homogeneous_process_events_optimized(f2, l, t)) for _ in range(sz)])\n",
    "    print(f\"    Actual mean: {mean}\")\n",
    "\n",
    "    print(f\"Function (iii): x/2-1 if 2 <= x <= 3 else 1-x/6 with x into [2, 6] and with intervals [2+1/3, 2+2/3, 3, 3+1/3, 3+2/3, 4, 4+1/3, 4+2/3, 5, 5+1/3, 5+2/3, 6]\")\n",
    "    t = [2+1/3, 2+2/3, 3, 3+1/3, 3+2/3, 4, 4+1/3, 4+2/3, 5, 5+1/3, 5+2/3, 6]\n",
    "    l = [f3(2+1/3), f3(2+2/3), f3(3), f3(3), f3(3+1/3), f3(3+2/3), f3(4), f3(4+1/3), f3(4+2/3), f3(5), f3(5+1/3), f3(5+2/3)]\n",
    "    mean = np.mean([len(poisson_no_homogeneous_process_events_optimized(f3, l, t)) for _ in range(sz)])\n",
    "    print(f\"    Actual mean: {mean}\")\n",
    "    print()\n",
    "\n",
    "ej15_graphic_representation()\n",
    "ej15_itemA()\n",
    "ej15_itemB()\n"
   ]
  }
 ],
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    "name": "ipython",
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