R1UnivariateScaledExponential.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.  * 
  11.  *  This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
  12.  *      asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
  13.  *      analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
  14.  *      equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
  15.  *      numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
  16.  *      and computational support.
  17.  *  
  18.  *      https://lakshmidrip.github.io/DROP/
  19.  *  
  20.  *  DROP is composed of three modules:
  21.  *  
  22.  *  - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
  23.  *  - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
  24.  *  - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
  25.  * 
  26.  *  DROP Product Core implements libraries for the following:
  27.  *  - Fixed Income Analytics
  28.  *  - Loan Analytics
  29.  *  - Transaction Cost Analytics
  30.  * 
  31.  *  DROP Portfolio Core implements libraries for the following:
  32.  *  - Asset Allocation Analytics
  33.  *  - Asset Liability Management Analytics
  34.  *  - Capital Estimation Analytics
  35.  *  - Exposure Analytics
  36.  *  - Margin Analytics
  37.  *  - XVA Analytics
  38.  * 
  39.  *  DROP Computational Core implements libraries for the following:
  40.  *  - Algorithm Support
  41.  *  - Computation Support
  42.  *  - Function Analysis
  43.  *  - Model Validation
  44.  *  - Numerical Analysis
  45.  *  - Numerical Optimizer
  46.  *  - Spline Builder
  47.  *  - Statistical Learning
  48.  * 
  49.  *  Documentation for DROP is Spread Over:
  50.  * 
  51.  *  - Main                     => https://lakshmidrip.github.io/DROP/
  52.  *  - Wiki                     => https://github.com/lakshmiDRIP/DROP/wiki
  53.  *  - GitHub                   => https://github.com/lakshmiDRIP/DROP
  54.  *  - Repo Layout Taxonomy     => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
  55.  *  - Javadoc                  => https://lakshmidrip.github.io/DROP/Javadoc/index.html
  56.  *  - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
  57.  *  - Release Versions         => https://lakshmidrip.github.io/DROP/version.html
  58.  *  - Community Credits        => https://lakshmidrip.github.io/DROP/credits.html
  59.  *  - Issues Catalog           => https://github.com/lakshmiDRIP/DROP/issues
  60.  *  - JUnit                    => https://lakshmidrip.github.io/DROP/junit/index.html
  61.  *  - Jacoco                   => https://lakshmidrip.github.io/DROP/jacoco/index.html
  62.  * 
  63.  *  Licensed under the Apache License, Version 2.0 (the "License");
  64.  *      you may not use this file except in compliance with the License.
  65.  *   
  66.  *  You may obtain a copy of the License at
  67.  *      http://www.apache.org/licenses/LICENSE-2.0
  68.  *  
  69.  *  Unless required by applicable law or agreed to in writing, software
  70.  *      distributed under the License is distributed on an "AS IS" BASIS,
  71.  *      WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  72.  *  
  73.  *  See the License for the specific language governing permissions and
  74.  *      limitations under the License.
  75.  */

  77. /**
  78.  * <i>R1UnivariateScaledExponential</i> implements the Probability Density Function for the Scaled Univariate
  79.  *  R<sup>1</sup> Exponential Function. The References are:
  80.  * 
  81.  * <br><br>
  82.  *  <ul>
  83.  *      <li>
  84.  *          Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
  85.  *              <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
  86.  *      </li>
  87.  *      <li>
  88.  *          Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye
  89.  *              Susceptibilities in Glassy Systems <i>Physical Review E</i> <b>65 (6)</b> 061510
  90.  *      </li>
  91.  *      <li>
  92.  *          Wikipedia (2019): Stretched Exponential Function
  93.  *              https://en.wikipedia.org/wiki/Stretched_exponential_function
  94.  *      </li>
  95.  *      <li>
  96.  *          Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic
  97.  *              Error-Bounds, Double Exponential Transform, and Open Source Implementation <i>libkw</i>
  98.  *              <i>Algorithm</i> <b>5 (4)</b> 604-628
  99.  *      </li>
  100.  *      <li>
  101.  *          Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions <i>Journal of Chemical
  102.  *              Physics</i> <b>116 (8)</b> 3204-3209
  103.  *      </li>
  104.  *  </ul>
  105.  *
  106.  *  <br><br>
  107.  *  <ul>
  108.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  109.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  110.  *      <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>
  111.  *      <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>
  112.  *  </ul>
  113.  *
  114.  * @author Lakshmi Krishnamurthy
  115.  */

  117. public class R1UnivariateScaledExponential extends org.drip.measure.continuous.R1Univariate
  118. {
  119.     private double _normalizer = java.lang.Double.NaN;
  120.     private org.drip.function.definition.R1ToR1 _gammaEstimator = null;
  121.     private org.drip.specialfunction.definition.ScaledExponentialEstimator _scaledExponentialEstimator =
  122.         null;

  124.     /**
  125.      * UnivariateScaledExponential Constructor
  126.      * 
  127.      * @param scaledExponentialEstimator Scaled Exponential Estimator
  128.      * @param gammaEstimator Gamma Estimator
  129.      * 
  130.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  131.      */

  133.     public R1UnivariateScaledExponential (
  134.         final org.drip.specialfunction.definition.ScaledExponentialEstimator scaledExponentialEstimator,
  135.         final org.drip.function.definition.R1ToR1 gammaEstimator)
  136.         throws java.lang.Exception
  137.     {
  138.         if (null == (_scaledExponentialEstimator = scaledExponentialEstimator) ||
  139.             null == (_gammaEstimator = gammaEstimator))
  140.         {
  141.             throw new java.lang.Exception ("R1UnivariateScaledExponential Constructor => Invalid Inputs");
  142.         }

  144.         _normalizer = 1. / _gammaEstimator.evaluate (1. + (1. / _scaledExponentialEstimator.exponent())) /
  145.             _scaledExponentialEstimator.characteristicRelaxationTime();
  146.     }

  148.     /**
  149.      * Retrieve the Scaled Exponential Estimator
  150.      * 
  151.      * @return Scaled Exponential Estimator
  152.      */

  154.     public org.drip.specialfunction.definition.ScaledExponentialEstimator scaledExponentialEstimator()
  155.     {
  156.         return _scaledExponentialEstimator;
  157.     }

  159.     /**
  160.      * Retrieve the Gamma Estimator
  161.      * 
  162.      * @return Gamma Estimator
  163.      */

  165.     public org.drip.function.definition.R1ToR1 gammaEstimator()
  166.     {
  167.         return _gammaEstimator;
  168.     }

  170.     @Override public double[] support()
  171.     {
  172.         return new double[]
  173.         {
  174.             0.,
  175.             java.lang.Double.POSITIVE_INFINITY
  176.         };
  177.     }

  179.     @Override public double density (
  180.         final double t)
  181.         throws java.lang.Exception
  182.     {
  183.         return _scaledExponentialEstimator.evaluate (t) * _normalizer;
  184.     }

  186.     @Override public double cumulative (
  187.         final double t)
  188.         throws java.lang.Exception
  189.     {
  190.         if (!supported (t))
  191.         {
  192.             throw new java.lang.Exception ("R1UnivariateScaledExponential::cumulative => Invalid Inputs");
  193.         }

  195.         return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (
  196.             0.,
  197.             t,
  198.             100
  199.         ).integrate (
  200.             new org.drip.function.definition.R1ToR1 (null)
  201.             {
  202.                 @Override public double evaluate (
  203.                     final double u)
  204.                     throws java.lang.Exception
  205.                 {
  206.                     return java.lang.Double.isInfinite (u) || 0. == u ? 0. :
  207.                         _scaledExponentialEstimator.evaluate (u);
  208.                 }
  209.             }
  210.         ) * _normalizer;
  211.     }

  213.     @Override public double incremental (
  214.         final double t1,
  215.         final double t2)
  216.         throws java.lang.Exception
  217.     {
  218.         if (!org.drip.numerical.common.NumberUtil.IsValid (t1) || 0. > t1 ||
  219.             !org.drip.numerical.common.NumberUtil.IsValid (t2) || t1 > t2)
  220.         {
  221.             throw new java.lang.Exception ("R1UnivariateScaledExponential::incremental => Invalid Inputs");
  222.         }

  224.         return org.drip.numerical.integration.NewtonCotesQuadratureGenerator.Zero_PlusOne (
  225.             t1,
  226.             t2,
  227.             100
  228.         ).integrate (
  229.             new org.drip.function.definition.R1ToR1 (null)
  230.             {
  231.                 @Override public double evaluate (
  232.                     final double u)
  233.                     throws java.lang.Exception
  234.                 {
  235.                     return java.lang.Double.isInfinite (u) || 0. == u ? 0. :
  236.                         _scaledExponentialEstimator.evaluate (u);
  237.                 }
  238.             }
  239.         ) * _normalizer;
  240.     }

  242.     @Override public double mean()
  243.         throws java.lang.Exception
  244.     {
  245.         return _scaledExponentialEstimator.firstMoment (_gammaEstimator) * _normalizer;
  246.     }

  248.     @Override public double variance()
  249.         throws java.lang.Exception
  250.     {
  251.         try
  252.         {
  253.             double mean = _scaledExponentialEstimator.firstMoment (_gammaEstimator) * _normalizer;

  255.             return _scaledExponentialEstimator.higherMoment (
  256.                 2,
  257.                 _gammaEstimator
  258.             ) * _normalizer * _normalizer - mean * mean;
  259.         }
  260.         catch (java.lang.Exception e)
  261.         {
  262.             e.printStackTrace();
  263.         }

  265.         return java.lang.Double.NaN;
  266.     }

  268.     /**
  269.      * Retrieve the Normalizer
  270.      * 
  271.      * @return Normalizer
  272.      */

  274.     public double normalizer()
  275.     {
  276.         return _normalizer;
  277.     }

  279.     /**
  280.      * Retrieve the "Lambda" Parameter
  281.      * 
  282.      * @return "Lambda" Parameter
  283.      */

  285.     public double lambda()
  286.     {
  287.         return 1. / _scaledExponentialEstimator.characteristicRelaxationTime();
  288.     }
  289. }
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