UnivariateMoments.java

  1. package org.drip.measure.statistics;

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

  80. /**
  81.  * <i>UnivariateMoments</i> generates and holds the Specified Univariate Series Mean, Variance, and a few
  82.  * selected Moments.
  83.  *
  84.  *  <br><br>
  85.  *  <ul>
  86.  *      <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
  87.  *      <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
  88.  *      <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>
  89.  *      <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/statistics/README.md">R<sup>1</sup> R<sup>d</sup> Thin Thick Moments</a></li>
  90.  *  </ul>
  91.  *
  92.  * @author Lakshmi Krishnamurthy
  93.  */

  95. public class UnivariateMoments {
  96.     private int _iNumSample = 0;
  97.     private java.lang.String _strName = "";
  98.     private double _dblMean = java.lang.Double.NaN;
  99.     private double _dblVariance = java.lang.Double.NaN;
  100.     private java.util.Map<java.lang.Integer, java.lang.Double> _mapMoment = null;

  102.     /**
  103.      * Construct a UnivariateMoments Instance for the specified Series
  104.      * 
  105.      * @param strName Series Name
  106.      * @param adblEntry Series Entry
  107.      * @param aiMoment Array of Moments to be Calculated
  108.      * 
  109.      * @return The UnivariateMoments Instance
  110.      */

  112.     public static final UnivariateMoments Standard (
  113.         final java.lang.String strName,
  114.         final double[] adblEntry,
  115.         final int[] aiMoment)
  116.     {
  117.         if (null == adblEntry) return null;

  119.         double dblMean = 0.;
  120.         double dblVariance = 0.;
  121.         int iNumSample = adblEntry.length;
  122.         int iNumMoment = null == aiMoment ? 0 : aiMoment.length;
  123.         double[] adblMoment = 0 == iNumMoment ? null : new double[iNumMoment];

  125.         java.util.Map<java.lang.Integer, java.lang.Double> mapMoment = 0 == iNumMoment ? null : new
  126.             java.util.TreeMap<java.lang.Integer, java.lang.Double>();

  128.         if (0 == iNumSample) return null;

  130.         for (int i = 0; i < iNumSample; ++i) {
  131.             if (!org.drip.numerical.common.NumberUtil.IsValid (adblEntry[i])) return null;

  133.             dblMean += adblEntry[i];
  134.         }

  136.         dblMean /= iNumSample;

  138.         for (int j = 0; j < iNumMoment; ++j)
  139.             adblMoment[j] = 0.;

  141.         for (int i = 0; i < iNumSample; ++i) {
  142.             double dblError = dblMean - adblEntry[i];
  143.             dblVariance += (dblError * dblError);

  145.             for (int j = 0; j < iNumMoment; ++j)
  146.                 adblMoment[j] = adblMoment[j] + java.lang.Math.pow (dblError, aiMoment[j]);
  147.         }

  149.         for (int j = 0; j < iNumMoment; ++j)
  150.             mapMoment.put (aiMoment[j], adblMoment[j]);

  152.         try {
  153.             return new UnivariateMoments (strName, dblMean, dblVariance / iNumSample, iNumSample, mapMoment);
  154.         } catch (java.lang.Exception e) {
  155.             e.printStackTrace();
  156.         }

  158.         return null;
  159.     }

  161.     /**
  162.      * Construct a UnivariateMoments Instance for the specified Series
  163.      * 
  164.      * @param strName Series Name
  165.      * @param adblEntry Series Entry
  166.      * 
  167.      * @return The UnivariateMoments Instance
  168.      */

  170.     public static final UnivariateMoments Standard (
  171.         final java.lang.String strName,
  172.         final double[] adblEntry)
  173.     {
  174.         return Standard (strName, adblEntry, null);
  175.     }

  177.     protected UnivariateMoments (
  178.         final java.lang.String strName,
  179.         final double dblMean,
  180.         final double dblVariance,
  181.         final int iNumSample,
  182.         final java.util.Map<java.lang.Integer, java.lang.Double> mapMoment)
  183.         throws java.lang.Exception
  184.     {
  185.         if (null == (_strName = strName) || _strName.isEmpty() || !org.drip.numerical.common.NumberUtil.IsValid
  186.             (_dblMean = dblMean) || !org.drip.numerical.common.NumberUtil.IsValid (_dblVariance = dblVariance) ||
  187.                 0 >= (_iNumSample = iNumSample))
  188.             throw new java.lang.Exception ("UnivariateMetrics Constructor => Invalid Inputs!");

  190.         _mapMoment = mapMoment;
  191.     }

  193.     /**
  194.      * Retrieve the Series Name
  195.      * 
  196.      * @return The Series Name
  197.      */

  199.     public java.lang.String name()
  200.     {
  201.         return _strName;
  202.     }

  204.     /**
  205.      * Retrieve the Number of Samples
  206.      * 
  207.      * @return The Number of Samples
  208.      */

  210.     public int numSample()
  211.     {
  212.         return _iNumSample;
  213.     }

  215.     /**
  216.      * Retrieve the Series Mean
  217.      * 
  218.      * @return The Series Mean
  219.      */

  221.     public double mean()
  222.     {
  223.         return _dblMean;
  224.     }

  226.     /**
  227.      * Retrieve the Series Variance
  228.      * 
  229.      * @return The Series Variance
  230.      */

  232.     public double variance()
  233.     {
  234.         return _dblVariance;
  235.     }

  237.     /**
  238.      * Retrieve the Series Standard Deviation
  239.      * 
  240.      * @return The Series Standard Deviation
  241.      */

  243.     public double stdDev()
  244.     {
  245.         return java.lang.Math.sqrt (_dblVariance);
  246.     }

  248.     /**
  249.      * Retrieve the Series Standard Error
  250.      * 
  251.      * @return The Series Standard Error
  252.      */

  254.     public double stdError()
  255.     {
  256.         return java.lang.Math.sqrt (_dblVariance);
  257.     }

  259.     /**
  260.      * Retrieve the Moments Map
  261.      * 
  262.      * @return The Map of Moments
  263.      */

  265.     public java.util.Map<java.lang.Integer, java.lang.Double> momentMap()
  266.     {
  267.         return _mapMoment;
  268.     }

  270.     /**
  271.      * Compute the Series t-Statistic around the Series Hypothesis Pivot
  272.      * 
  273.      * @param hypothesisPivot The Series Hypothesis Pivot
  274.      * 
  275.      * @return The Series t-Statistic around the Series Hypothesis Pivot
  276.      * 
  277.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  278.      */

  280.     public double tStatistic (
  281.         final double hypothesisPivot)
  282.         throws java.lang.Exception
  283.     {
  284.         if (!org.drip.numerical.common.NumberUtil.IsValid (hypothesisPivot))
  285.         {
  286.             throw new java.lang.Exception ("UnivariateMetrics::tStatistic => Invalid Inputs");
  287.         }

  289.         return (_dblMean - hypothesisPivot) / java.lang.Math.sqrt (_dblVariance);
  290.     }

  292.     /**
  293.      * Compute the Series t-Statistic for Hypothesis Pivot = 0 (e.g., the False Positive NULL Hypothesis for
  294.      *  for Homoscedastic Univariate Linear Regression)
  295.      * 
  296.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  297.      * 
  298.      * @return The Series t-Statistic
  299.      */

  301.     public double tStatistic()
  302.         throws java.lang.Exception
  303.     {
  304.         return _dblMean / java.lang.Math.sqrt (_dblVariance);
  305.     }

  307.     /**
  308.      * Estimate the Offset in Terms of the NUmber of Standard Errors
  309.      * 
  310.      * @param x The Observation Point
  311.      * 
  312.      * @return The Offset in Terms of the NUmber of Standard Errors
  313.      * 
  314.      * @throws java.lang.Exception Thrown if the Inputs are Invalid
  315.      */

  317.     public double standardErrorOffset (
  318.         final double x)
  319.         throws java.lang.Exception
  320.     {
  321.         if (!org.drip.numerical.common.NumberUtil.IsValid (x))
  322.         {
  323.             throw new java.lang.Exception ("UnivariateMetrics::standardErrorOffset => Invalid Inputs");
  324.         }

  326.         return (_dblMean - x) / java.lang.Math.sqrt (_dblVariance);
  327.     }

  329.     /**
  330.      * Retrieve the Degrees of Freedom
  331.      * 
  332.      * @return The Degrees of Freedom
  333.      */

  335.     public int degreesOfFreedom()
  336.     {
  337.         return _iNumSample - 1;
  338.     }

  340.     /**
  341.      * Compute the Predictive Confidence Level
  342.      * 
  343.      * @return The Predictive Confidence Level
  344.      */

  346.     public double predictiveConfidenceLevel()
  347.     {
  348.         return java.lang.Math.sqrt (_dblVariance * (1. + 1. / (1. + _iNumSample)));
  349.     }
  350. }
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