R1Univariate.java

  1. package org.drip.measure.continuous;

  3. /*
  4.  * -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
  5.  */

  7. /*!
  8.  * Copyright (C) 2020 Lakshmi Krishnamurthy
  9.  * Copyright (C) 2019 Lakshmi Krishnamurthy
  10.  * Copyright (C) 2018 Lakshmi Krishnamurthy
  11.  * Copyright (C) 2017 Lakshmi Krishnamurthy
  12.  * Copyright (C) 2016 Lakshmi Krishnamurthy
  13.  * Copyright (C) 2015 Lakshmi Krishnamurthy
  14.  * Copyright (C) 2014 Lakshmi Krishnamurthy
  15.  * Copyright (C) 2013 Lakshmi Krishnamurthy
  16.  * 
  17.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  18.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  19.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  20.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  21.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  22.  *      and computational support.
  23.  *  
  24.  *      https://lakshmidrip.github.io/DROP/
  25.  *  
  26.  *  DROP is composed of three modules:
  27.  *  
  28.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  29.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  30.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  31.  * 
  32.  *  DROP Product Core implements libraries for the following:
  33.  *  - Fixed Income Analytics
  34.  *  - Loan Analytics
  35.  *  - Transaction Cost Analytics
  36.  * 
  37.  *  DROP Portfolio Core implements libraries for the following:
  38.  *  - Asset Allocation Analytics
  39.  *  - Asset Liability Management Analytics
  40.  *  - Capital Estimation Analytics
  41.  *  - Exposure Analytics
  42.  *  - Margin Analytics
  43.  *  - XVA Analytics
  44.  * 
  45.  *  DROP Computational Core implements libraries for the following:
  46.  *  - Algorithm Support
  47.  *  - Computation Support
  48.  *  - Function Analysis
  49.  *  - Model Validation
  50.  *  - Numerical Analysis
  51.  *  - Numerical Optimizer
  52.  *  - Spline Builder
  53.  *  - Statistical Learning
  54.  * 
  55.  *  Documentation for DROP is Spread Over:
  56.  * 
  57.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  58.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  59.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  60.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  61.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  62.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  63.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  64.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  65.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  66.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  67.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  68.  * 
  69.  *  Licensed under the Apache License, Version 2.0 (the "License");
  70.  *      you may not use this file except in compliance with the License.
  71.  *   
  72.  *  You may obtain a copy of the License at
  73.  *      http://www.apache.org/licenses/LICENSE-2.0
  74.  *  
  75.  *  Unless required by applicable law or agreed to in writing, software
  76.  *      distributed under the License is distributed on an "AS IS" BASIS,
  77.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  78.  *  
  79.  *  See the License for the specific language governing permissions and
  80.  *      limitations under the License.
  81.  */

  83. /**
  84.  * <i>R1Univariate</i> exposes the Base Abstract Class behind Univariate R<sup>1</sup> Distributions. It
  85.  *  exports the Methods for incremental, cumulative, and inverse cumulative distribution densities.
  86.  *
  87.  *  <br><br>
  88.  *  <ul>
  89.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  90.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  91.  *      <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/README.md">R<sup>d</sup> Continuous/Discrete Probability Measures</a></li>
  92.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/continuous/README.md">R<sup>1</sup> and R<sup>d</sup> Continuous Random Measure</a></li>
  93.  *  </ul>
  94.  *
  95.  * @author Lakshmi Krishnamurthy
  96.  */

  98. public abstract class R1Univariate {

  100.     /**
  101.      * Lay out the Support of the PDF Range
  102.      * 
  103.      * @return Support of the PDF Range
  104.      */

  106.     public abstract double[] support();

  108.     /**
  109.      * Indicate if x is inside the Supported Range
  110.      * 
  111.      * @param x X
  112.      * 
  113.      * @return TRUE - x is inside of the Supported Range
  114.      */

  116.     public boolean supported (
  117.         final double x)
  118.     {
  119.         if (java.lang.Double.isNaN (x))
  120.         {
  121.             return false;
  122.         }

  124.         double[] range = support();

  126.         return range[0] <= x && x <= range[1];
  127.     }

  129.     /**
  130.      * Compute the Density under the Distribution at the given Variate
  131.      * 
  132.      * @param dblX Variate at which the Density needs to be computed
  133.      * 
  134.      * @return The Density
  135.      * 
  136.      * @throws java.lang.Exception Thrown if the input is invalid
  137.      */

  139.     public abstract double density (
  140.         final double dblX)
  141.         throws java.lang.Exception;

  143.     /**
  144.      * Compute the cumulative under the distribution to the given value
  145.      * 
  146.      * @param dblX Variate to which the cumulative is to be computed
  147.      * 
  148.      * @return The cumulative
  149.      * 
  150.      * @throws java.lang.Exception Thrown if the inputs are invalid
  151.      */

  153.     public abstract double cumulative (
  154.         final double dblX)
  155.         throws java.lang.Exception;

  157.     /**
  158.      * Compute the Incremental under the Distribution between the 2 variates
  159.      * 
  160.      * @param dblXLeft Left Variate to which the cumulative is to be computed
  161.      * @param dblXRight Right Variate to which the cumulative is to be computed
  162.      * 
  163.      * @return The Incremental under the Distribution between the 2 variates
  164.      * 
  165.      * @throws java.lang.Exception Thrown if the inputs are invalid
  166.      */

  168.     public double incremental (
  169.         final double dblXLeft,
  170.         final double dblXRight)
  171.         throws java.lang.Exception
  172.     {
  173.         return cumulative (dblXRight) - cumulative (dblXLeft);
  174.     }

  176.     /**
  177.      * Compute the inverse cumulative under the distribution corresponding to the given value
  178.      * 
  179.      * @param p Value corresponding to which the inverse cumulative is to be computed
  180.      * 
  181.      * @return The inverse cumulative
  182.      * 
  183.      * @throws java.lang.Exception Thrown if the Input is invalid
  184.      */

  186.     public double invCumulative (
  187.         final double p)
  188.         throws java.lang.Exception
  189.     {
  190.         if (!org.drip.numerical.common.NumberUtil.IsValid (p) || 0. > p || 1. < p)
  191.         {
  192.             throw new java.lang.Exception ("R1Univariate::invCumulative => Invalid Inputs");
  193.         }

  195.         org.drip.function.r1tor1solver.FixedPointFinderOutput fixedPointFinderOutput =
  196.             new org.drip.function.r1tor1solver.FixedPointFinderBrent (
  197.                 0.,
  198.                 new org.drip.function.definition.R1ToR1 (null)
  199.                 {
  200.                     @Override public double evaluate (
  201.                         final double u)
  202.                         throws java.lang.Exception
  203.                     {
  204.                         return cumulative (u) - p;
  205.                     }
  206.                 },
  207.                 true
  208.             ).findRoot();

  210.         if (null == fixedPointFinderOutput)
  211.         {
  212.             throw new java.lang.Exception ("R1Univariate::invCumulative => Cannot find Root");
  213.         }

  215.         return fixedPointFinderOutput.getRoot();
  216.     }

  218.     /**
  219.      * Retrieve the Mean of the Distribution
  220.      * 
  221.      * @return The Mean of the Distribution
  222.      * 
  223.      * @throws java.lang.Exception Thrown if the Mean cannot be estimated
  224.      */

  226.     public abstract double mean()
  227.         throws java.lang.Exception;

  229.     /**
  230.      * Retrieve the Median of the Distribution
  231.      * 
  232.      * @return The Median of the Distribution
  233.      * 
  234.      * @throws java.lang.Exception Thrown if the Median cannot be estimated
  235.      */

  237.     public double median()
  238.         throws java.lang.Exception
  239.     {
  240.         return invCumulative (0.50);
  241.     }

  243.     /**
  244.      * Retrieve the Mode of the Distribution
  245.      * 
  246.      * @return The Mode of the Distribution
  247.      * 
  248.      * @throws java.lang.Exception Thrown if the Mode cannot be estimated
  249.      */

  251.     public double mode()
  252.         throws java.lang.Exception
  253.     {
  254.         final org.drip.function.definition.R1ToR1 densityFunction =
  255.             new org.drip.function.definition.R1ToR1 (null)
  256.         {
  257.             @Override public double evaluate (
  258.                 final double u)
  259.                 throws java.lang.Exception
  260.             {
  261.                 return density (u);
  262.             }
  263.         };

  265.         org.drip.function.r1tor1solver.FixedPointFinderOutput fixedPointFinderOutput =
  266.             new org.drip.function.r1tor1solver.FixedPointFinderBrent (
  267.                 0.,
  268.                 new org.drip.function.definition.R1ToR1 (null)
  269.                 {
  270.                     @Override public double evaluate (
  271.                         final double u)
  272.                         throws java.lang.Exception
  273.                     {
  274.                         return densityFunction.derivative (
  275.                             u,
  276.                             1
  277.                         );
  278.                     }
  279.                 },
  280.                 true
  281.             ).findRoot();

  283.         if (null == fixedPointFinderOutput)
  284.         {
  285.             throw new java.lang.Exception ("R1Univariate::invCumulative => Cannot find Root");
  286.         }

  288.         return fixedPointFinderOutput.getRoot();
  289.     }

  291.     /**
  292.      * Retrieve the Variance of the Distribution
  293.      * 
  294.      * @return The Variance of the Distribution
  295.      * 
  296.      * @throws java.lang.Exception Thrown if the Variance cannot be estimated
  297.      */

  299.     public abstract double variance()
  300.         throws java.lang.Exception;

  302.     /**
  303.      * Retrieve the Skewness of the Distribution
  304.      * 
  305.      * @return The Skewness of the Distribution
  306.      * 
  307.      * @throws java.lang.Exception Thrown if the Skewness cannot be estimated
  308.      */

  310.     public double skewness()
  311.         throws java.lang.Exception
  312.     {
  313.         throw new java.lang.Exception ("R1Univariate::skewness => Not implemented");
  314.     }

  316.     /**
  317.      * Retrieve the Excess Kurtosis of the Distribution
  318.      * 
  319.      * @return The Excess Kurtosis of the Distribution
  320.      * 
  321.      * @throws java.lang.Exception Thrown if the Skewness cannot be estimated
  322.      */

  324.     public double excessKurtosis()
  325.         throws java.lang.Exception
  326.     {
  327.         throw new java.lang.Exception ("R1Univariate::excessKurtosis => Not implemented");
  328.     }

  330.     /**
  331.      * Retrieve the Differential Entropy of the Distribution
  332.      * 
  333.      * @return The Differential Entropy of the Distribution
  334.      * 
  335.      * @throws java.lang.Exception Thrown if the Entropy cannot be estimated
  336.      */

  338.     public double differentialEntropy()
  339.         throws java.lang.Exception
  340.     {
  341.         return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.GaussLaguerreLeftDefinite (
  342.             0.,
  343.             10000
  344.         ).integrate (
  345.             new org.drip.function.definition.R1ToR1 (null)
  346.             {
  347.                 @Override public double evaluate (
  348.                     final double t)
  349.                     throws java.lang.Exception
  350.                 {
  351.                     double density = density (t);

  353.                     return density * java.lang.Math.log (density);
  354.                 }
  355.             }
  356.         );
  357.     }

  359.     /**
  360.      * Construct the Moment Generating Function
  361.      * 
  362.      * @return The Moment Generating Function
  363.      */

  365.     public org.drip.function.definition.R1ToR1 momentGeneratingFunction()
  366.     {
  367.         return null;
  368.     }

  370.     /**
  371.      * Construct the Probability Generating Function
  372.      * 
  373.      * @return The Probability Generating Function
  374.      */

  376.     public org.drip.function.definition.R1ToR1 probabilityGeneratingFunction()
  377.     {
  378.         return null;
  379.     }

  381.     /**
  382.      * Generate a Random Variable corresponding to the Distribution
  383.      * 
  384.      * @return Random Variable corresponding to the Distribution
  385.      * 
  386.      * @throws java.lang.Exception Thrown if the Random Instance cannot be estimated
  387.      */

  389.     public double random()
  390.         throws java.lang.Exception
  391.     {
  392.         return invCumulative (java.lang.Math.random());
  393.     }

  395.     /**
  396.      * Retrieve the Array of Generated Random Variables
  397.      * 
  398.      * @param arrayCount Number of Elements
  399.      * 
  400.      * @return Array of Generated Random Variables
  401.      */

  403.     public double[] randomArray (
  404.         final int arrayCount)
  405.     {
  406.         if (0 >= arrayCount)
  407.         {
  408.             return null;
  409.         }

  411.         double[] randomArray = new double[arrayCount];

  413.         for (int index = 0; index < arrayCount; ++index)
  414.         {
  415.             try
  416.             {
  417.                 randomArray[index] = random();
  418.             }
  419.             catch (java.lang.Exception e)
  420.             {
  421.                 e.printStackTrace();

  423.                 return null;
  424.             }
  425.         }

  427.         return randomArray;
  428.     }

  430.     /**
  431.      * Retrieve the Population Central Measures
  432.      * 
  433.      * @return The Population Central Measures
  434.      */

  436.     public org.drip.measure.statistics.PopulationCentralMeasures populationCentralMeasures()
  437.     {
  438.         try
  439.         {
  440.             return new org.drip.measure.statistics.PopulationCentralMeasures (
  441.                 mean(),
  442.                 variance()
  443.             );
  444.         }
  445.         catch (java.lang.Exception e)
  446.         {
  447.             e.printStackTrace();
  448.         }

  450.         return null;
  451.     }

  453.     /**
  454.      * Retrieve the Univariate Weighted Histogram
  455.      * 
  456.      * @return The Univariate Weighted Histogram
  457.      */

  459.     public org.drip.numerical.common.Array2D histogram()
  460.     {
  461.         return null;
  462.     }
  463. }
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