PoissonDistribution.java

  1. package org.drip.measure.discrete;

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

  81. /**
  82.  * <i>PoissonDistribution</i> implements the Univariate Poisson Distribution using the specified
  83.  * Mean/Variance.
  84.  *
  85.  *  <br><br>
  86.  *  <ul>
  87.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  88.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  89.  *      <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>
  90.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/discrete/README.md">Antithetic, Quadratically Re-sampled, De-biased Distribution</a></li>
  91.  *  </ul>
  92.  *
  93.  * @author Lakshmi Krishnamurthy
  94.  */

  96. public class PoissonDistribution extends org.drip.measure.continuous.R1Univariate {
  97.     private double _dblLambda = java.lang.Double.NaN;
  98.     private double _dblExponentialLambda = java.lang.Double.NaN;

  100.     /**
  101.      * Construct a PoissonDistribution Instance
  102.      * 
  103.      * @param dblLambda Lambda
  104.      * 
  105.      * @throws java.lang.Exception Thrown if the inputs are invalid
  106.      */

  108.     public PoissonDistribution (
  109.         final double dblLambda)
  110.         throws java.lang.Exception
  111.     {
  112.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblLambda = dblLambda) || 0. >= _dblLambda)
  113.             throw new java.lang.Exception ("PoissonDistribution constructor: Invalid inputs");

  115.         _dblExponentialLambda = java.lang.Math.exp (-1. * _dblLambda);
  116.     }

  118.     /**
  119.      * Retrieve Lambda
  120.      * 
  121.      * @return Lambda
  122.      */

  124.     public double lambda()
  125.     {
  126.         return _dblLambda;
  127.     }

  129.     @Override public double[] support()
  130.     {
  131.         return new double[]
  132.         {
  133.             0.,
  134.             java.lang.Double.POSITIVE_INFINITY
  135.         };
  136.     }

  138.     @Override public double cumulative (
  139.         final double dblX)
  140.         throws java.lang.Exception
  141.     {
  142.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  143.             throw new java.lang.Exception ("PoissonDistribution::cumulative => Invalid inputs");

  145.         int iEnd = (int) dblX;
  146.         double dblYLocal = 1.;
  147.         double dblYCumulative = 0.;

  149.         for (int i = 1; i < iEnd; ++i) {
  150.             i = i + 1;
  151.             dblYLocal *= _dblLambda / i;
  152.             dblYCumulative += _dblExponentialLambda * dblYLocal;
  153.         }

  155.         return dblYCumulative;
  156.     }

  158.     @Override public double incremental (
  159.         final double dblXLeft,
  160.         final double dblXRight)
  161.         throws java.lang.Exception
  162.     {
  163.         return cumulative (dblXRight) - cumulative (dblXLeft);
  164.     }

  166.     @Override public double invCumulative (
  167.         final double dblY)
  168.         throws java.lang.Exception
  169.     {
  170.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblY))
  171.             throw new java.lang.Exception ("PoissonDistribution::invCumulative => Invalid inputs");

  173.         int i = 0;
  174.         double dblYLocal = 1.;
  175.         double dblYCumulative = 0.;

  177.         while (dblYCumulative < dblY) {
  178.             i = i + 1;
  179.             dblYLocal *= _dblLambda / i;
  180.             dblYCumulative += _dblExponentialLambda * dblYLocal;
  181.         }

  183.         return i - 1;
  184.     }

  186.     @Override public double density (
  187.         final double dblX)
  188.         throws java.lang.Exception
  189.     {
  190.         throw new java.lang.Exception
  191.             ("PoissonDistribution::density => Not available for discrete distributions");
  192.     }

  194.     @Override public double mean()
  195.     {
  196.         return _dblLambda;
  197.     }

  199.     @Override public double variance()
  200.     {
  201.         return _dblLambda;
  202.     }

  204.     @Override public org.drip.numerical.common.Array2D histogram()
  205.     {
  206.         return null;
  207.     }
  208. }
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