R1UnivariateNormal.java

  1. package org.drip.measure.gaussian;

  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>R1UnivariateNormal</i> implements the Univariate R<sup>1</sup> Normal Distribution. It implements the
  85.  * Incremental, the Cumulative, and the 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/gaussian/README.md">R<sup>1</sup> R<sup>d</sup> Covariant Gaussian Quadrature</a></li>
  93.  *  </ul>
  94.  *
  95.  * @author Lakshmi Krishnamurthy
  96.  */

  98. public class R1UnivariateNormal extends org.drip.measure.continuous.R1Univariate {
  99.     private double _dblMean = java.lang.Double.NaN;
  100.     private double _dblSigma = java.lang.Double.NaN;

  102.     /**
  103.      * Generate a N (0, 1) distribution
  104.      * 
  105.      * @return The N (0, 1) distribution
  106.      */

  108.     public static final org.drip.measure.gaussian.R1UnivariateNormal Standard()
  109.     {
  110.         try {
  111.             return new R1UnivariateNormal (0., 1.);
  112.         } catch (java.lang.Exception e) {
  113.             e.printStackTrace();
  114.         }

  116.         return null;
  117.     }

  119.     /**
  120.      * Construct a R1 Normal/Gaussian Distribution
  121.      * 
  122.      * @param dblMean Mean of the Distribution
  123.      * @param dblSigma Sigma of the Distribution
  124.      * 
  125.      * @throws java.lang.Exception Thrown if the inputs are invalid
  126.      */

  128.     public R1UnivariateNormal (
  129.         final double dblMean,
  130.         final double dblSigma)
  131.         throws java.lang.Exception
  132.     {
  133.         if (!org.drip.numerical.common.NumberUtil.IsValid (_dblMean = dblMean) ||
  134.             !org.drip.numerical.common.NumberUtil.IsValid (_dblSigma = dblSigma) || 0. > _dblSigma)
  135.             throw new java.lang.Exception ("R1UnivariateNormal Constructor: Invalid Inputs");
  136.     }

  138.     /**
  139.      * Retrieve the Sigma
  140.      * 
  141.      * @return The Sigma
  142.      */

  144.     public double sigma()
  145.     {
  146.         return _dblSigma;
  147.     }

  149.     @Override public double[] support()
  150.     {
  151.         return new double[]
  152.         {
  153.             java.lang.Double.NEGATIVE_INFINITY,
  154.             java.lang.Double.POSITIVE_INFINITY
  155.         };
  156.     }

  158.     @Override public double cumulative (
  159.         final double dblX)
  160.         throws java.lang.Exception
  161.     {
  162.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  163.             throw new java.lang.Exception ("R1UnivariateNormal::cumulative => Invalid Inputs");

  165.         if (0. == _dblSigma) return dblX >= _dblMean ? 1. : 0.;

  167.         return org.drip.measure.gaussian.NormalQuadrature.CDF ((dblX - _dblMean) / _dblSigma);
  168.     }

  170.     @Override public double incremental (
  171.         final double dblXLeft,
  172.         final double dblXRight)
  173.         throws java.lang.Exception
  174.     {
  175.         return cumulative (dblXRight) - cumulative (dblXLeft);
  176.     }

  178.     @Override public double invCumulative (
  179.         final double dblY)
  180.         throws java.lang.Exception
  181.     {
  182.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblY) || 0. == _dblSigma)
  183.             throw new java.lang.Exception ("R1UnivariateNormal::invCumulative => Cannot calculate");

  185.         return org.drip.measure.gaussian.NormalQuadrature.InverseCDF (dblY) * _dblSigma + _dblMean;
  186.     }

  188.     @Override public double density (
  189.         final double dblX)
  190.         throws java.lang.Exception
  191.     {
  192.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  193.             throw new java.lang.Exception ("R1UnivariateNormal::density => Invalid Inputs");

  195.         if (0. == _dblSigma) return dblX == _dblMean ? 1. : 0.;

  197.         double dblMeanShift = (dblX - _dblMean) / _dblSigma;

  199.         return java.lang.Math.exp (-0.5 * dblMeanShift * dblMeanShift);
  200.     }

  202.     @Override public double mean()
  203.     {
  204.         return _dblMean;
  205.     }

  207.     @Override public double median()
  208.     {
  209.         return _dblMean;
  210.     }

  212.     @Override public double mode()
  213.     {
  214.         return _dblMean;
  215.     }

  217.     @Override public double variance()
  218.     {
  219.         return _dblSigma * _dblSigma;
  220.     }

  222.     @Override public org.drip.numerical.common.Array2D histogram()
  223.     {
  224.         return null;
  225.     }

  227.     @Override public double random()
  228.     {
  229.         try
  230.         {
  231.             return invCumulative (java.lang.Math.random());
  232.         }
  233.         catch (java.lang.Exception e)
  234.         {
  235.             e.printStackTrace();
  236.         }

  238.         return java.lang.Double.NaN;
  239.     }

  241.     /**
  242.      * Compute the Error Function Around an Absolute Width around the Mean
  243.      * 
  244.      * @param dblX The Width
  245.      * 
  246.      * @return The Error Function Around an Absolute Width around the Mean
  247.      * 
  248.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  249.      */

  251.     public double errorFunction (
  252.         final double dblX)
  253.         throws java.lang.Exception
  254.     {
  255.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblX))
  256.             throw new java.lang.Exception ("R1UnivariateNormal::errorFunction => Invalid Inputs");

  258.         double dblWidth = java.lang.Math.abs (dblX);

  260.         return cumulative (_dblMean + dblWidth) - cumulative (_dblMean - dblWidth);
  261.     }

  263.     /**
  264.      * Compute the Confidence given the Width around the Mean
  265.      * 
  266.      * @param dblWidth The Width
  267.      * 
  268.      * @return The Error Function Around an Absolute Width around the Mean
  269.      * 
  270.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  271.      */

  273.     public double confidence (
  274.         final double dblWidth)
  275.         throws java.lang.Exception
  276.     {
  277.         return errorFunction (dblWidth);
  278.     }

  280.     /**
  281.      * Compute the Width around the Mean given the Confidence Level
  282.      * 
  283.      * @param dblConfidence The Confidence Level
  284.      * 
  285.      * @return The Width around the Mean given the Confidence Level
  286.      * 
  287.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  288.      */

  290.     public double confidenceInterval (
  291.         final double dblConfidence)
  292.         throws java.lang.Exception
  293.     {
  294.         if (!org.drip.numerical.common.NumberUtil.IsValid (dblConfidence) || 0. >= dblConfidence || 1. <=
  295.             dblConfidence)
  296.             throw new java.lang.Exception ("R1UnivariateNormal::confidenceInterval => Invalid Inputs");

  298.         return invCumulative (0.5 * (1. + dblConfidence));
  299.     }
  300. }
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