{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Maximum Likelihood Estimation on High Order Statistics\n",
    "In this notebook, we perform an analysis of time series data using the `xtremes` library. We utilize various estimators and statistical methods provided by the library to analyze and visualize the data.\n",
    "\n",
    "The following variables are used in this notebook:\n",
    "\n",
    "- **PWM**: A `PWM_estimators` object used for Probability Weighted Moments estimation.\n",
    "- **MLE**: A `ML_estimators` object used for Maximum Likelihood estimation.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import xtremes as xx\n",
    "import xtremes.topt as hos"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "TS = hos.TimeSeries(n=1000, modelparams=(0.5,0.1,0.1))\n",
    "TS.simulate(rep=200)\n",
    "TS.get_blockmaxima(block_size=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Probability Weighted Moments (PWM) Estimation\n",
    "\n",
    "In this section, we perform Probability Weighted Moments (PWM) estimation on the time series data. The `PWM_estimators` object is used for this purpose. Below are the steps involved:\n",
    "\n",
    "1. **Initialization**:\n",
    "    ```python\n",
    "    PWM = hos.PWM_estimators(TS)\n",
    "    ```\n",
    "    We initialize the `PWM_estimators` object with the time series data `TS`.\n",
    "\n",
    "2. **PWM Estimation**:\n",
    "    ```python\n",
    "    PWM.get_PWM_estimation()\n",
    "    ```\n",
    "    This method computes the PWM estimates for the given time series data.\n",
    "\n",
    "3. **Statistics Calculation**:\n",
    "    ```python\n",
    "    PWM.get_statistics(gamma_true=0)\n",
    "    ```\n",
    "    This method calculates the statistics based on the PWM estimates. Here, `gamma_true` is the true value of the shape parameter used for comparison.\n",
    "\n",
    "4. **Confidence Intervals**:\n",
    "    ```python\n",
    "    PWM.get_CIs()\n",
    "    ```\n",
    "    This method computes the confidence intervals for the PWM estimates.\n",
    "\n",
    "5. **View Statistics**:\n",
    "    ```python\n",
    "    PWM.statistics\n",
    "    ```\n",
    "    This attribute holds the computed statistics, which can be accessed for further analysis or visualization."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'gamma_mean': 0.47088517659996393,\n",
       " 'gamma_variance': 0.01670944312254425,\n",
       " 'gamma_bias': 0.029187884552301334,\n",
       " 'gamma_mse': 0.01756137572718272,\n",
       " 'mu_mean': 3.1883509998758033,\n",
       " 'mu_variance': 0.04162170110658726,\n",
       " 'sigma_mean': 1.598521986577066,\n",
       " 'sigma_variance': 0.05246458660618443,\n",
       " 'gamma_CI': array([0.26048308, 0.7876679 ]),\n",
       " 'mu_CI': array([2.85180707, 3.67041571]),\n",
       " 'sigma_CI': array([1.24809831, 2.0891756 ])}"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "PWM = hos.PWM_estimators(TS)\n",
    "PWM.get_PWM_estimation()\n",
    "PWM.get_statistics(gamma_true=0.5)\n",
    "PWM.get_CIs()\n",
    "PWM.statistics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plotting the distribution of the optained estimators together with a symmetrical CI is as easy as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "PWM.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The same works analogously for MLE. We use the PWM estimators as an initial guess for otimization. Instead of symmetrical CIs (default) we can also plot CIs with minimal width"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MLE = hos.ML_estimators(TS)\n",
    "MLE.get_ML_estimation(PWM_estimators= PWM)\n",
    "MLE.get_statistics(gamma_true=0)\n",
    "MLE.get_CIs(method='minimal_width')  \n",
    "MLE.plot()  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Maximum Likelihood Estimation (MLE) with Frechet Distribution\n",
    "\n",
    "In this section, we perform Maximum Likelihood Estimation (MLE) using the Frechet distribution on the time series data. The `Frechet_ML_estimators` object is used for this purpose. Below are the steps involved:\n",
    "\n",
    "1. **Initialization**:\n",
    "    ```python\n",
    "    MLE = hos.Frechet_ML_estimators(TS)\n",
    "    ```\n",
    "    We initialize the `Frechet_ML_estimators` object with the time series data `TS`.\n",
    "\n",
    "2. **MLE Estimation**:\n",
    "    ```python\n",
    "    MLE.get_ML_estimation(PWM_estimators= PWM)\n",
    "    ```\n",
    "    This method computes the MLE estimates for the given time series data using the PWM estimators as initial guesses for optimization.\n",
    "\n",
    "3. **Statistics Calculation**:\n",
    "    ```python\n",
    "    MLE.get_statistics(alpha_true=0)\n",
    "    ```\n",
    "    This method calculates the statistics based on the MLE estimates. Here, `alpha_true` is the true value of the shape parameter used for comparison.\n",
    "\n",
    "4. **Confidence Intervals**:\n",
    "    ```python\n",
    "    MLE.get_CIs()\n",
    "    ```\n",
    "    This method computes the confidence intervals for the MLE estimates.\n",
    "\n",
    "5. **View Statistics**:\n",
    "    ```python\n",
    "    MLE.plot()\n",
    "    ```\n",
    "    This method plots the distribution of the obtained estimators together with the confidence intervals.\n",
    "\n",
    "#### Difference between Frechet and GEV Distributions\n",
    "\n",
    "The key difference between using the Frechet distribution and the Generalized Extreme Value (GEV) distribution lies in the type of tail behavior they model:\n",
    "\n",
    "- **Frechet Distribution**: This distribution is used to model data with heavy tails. It is a special case of the GEV distribution with a positive shape parameter. The Frechet distribution is particularly useful for modeling extreme values that follow a power-law decay.\n",
    "\n",
    "- **GEV Distribution**: The GEV distribution is a more general form that encompasses three types of distributions based on the shape parameter: Gumbel (light tails), Frechet (heavy tails), and Weibull (bounded tails). The GEV distribution provides more flexibility in modeling different types of extreme value behavior.\n",
    "\n",
    "By using the `Frechet_ML_estimators`, we specifically focus on modeling heavy-tailed data, which is suitable for certain types of extreme value analysis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "MLE = hos.Frechet_ML_estimators(TS)\n",
    "MLE.get_ML_estimation(PWM_estimators= PWM)\n",
    "MLE.get_statistics(alpha_true=0)\n",
    "MLE.get_CIs()  \n",
    "MLE.plot()  "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "climaxtreme",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}