R1CentralFisherProxy.java
package org.drip.measure.chisquare;
/*
* -*- mode: java; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*-
*/
/*!
* Copyright (C) 2020 Lakshmi Krishnamurthy
* Copyright (C) 2019 Lakshmi Krishnamurthy
*
* This file is part of DROP, an open-source library targeting analytics/risk, transaction cost analytics,
* asset liability management analytics, capital, exposure, and margin analytics, valuation adjustment
* analytics, and portfolio construction analytics within and across fixed income, credit, commodity,
* equity, FX, and structured products. It also includes auxiliary libraries for algorithm support,
* numerical analysis, numerical optimization, spline builder, model validation, statistical learning,
* and computational support.
*
* https://lakshmidrip.github.io/DROP/
*
* DROP is composed of three modules:
*
* - DROP Product Core - https://lakshmidrip.github.io/DROP-Product-Core/
* - DROP Portfolio Core - https://lakshmidrip.github.io/DROP-Portfolio-Core/
* - DROP Computational Core - https://lakshmidrip.github.io/DROP-Computational-Core/
*
* DROP Product Core implements libraries for the following:
* - Fixed Income Analytics
* - Loan Analytics
* - Transaction Cost Analytics
*
* DROP Portfolio Core implements libraries for the following:
* - Asset Allocation Analytics
* - Asset Liability Management Analytics
* - Capital Estimation Analytics
* - Exposure Analytics
* - Margin Analytics
* - XVA Analytics
*
* DROP Computational Core implements libraries for the following:
* - Algorithm Support
* - Computation Support
* - Function Analysis
* - Model Validation
* - Numerical Analysis
* - Numerical Optimizer
* - Spline Builder
* - Statistical Learning
*
* Documentation for DROP is Spread Over:
*
* - Main => https://lakshmidrip.github.io/DROP/
* - Wiki => https://github.com/lakshmiDRIP/DROP/wiki
* - GitHub => https://github.com/lakshmiDRIP/DROP
* - Repo Layout Taxonomy => https://github.com/lakshmiDRIP/DROP/blob/master/Taxonomy.md
* - Javadoc => https://lakshmidrip.github.io/DROP/Javadoc/index.html
* - Technical Specifications => https://github.com/lakshmiDRIP/DROP/tree/master/Docs/Internal
* - Release Versions => https://lakshmidrip.github.io/DROP/version.html
* - Community Credits => https://lakshmidrip.github.io/DROP/credits.html
* - Issues Catalog => https://github.com/lakshmiDRIP/DROP/issues
* - JUnit => https://lakshmidrip.github.io/DROP/junit/index.html
* - Jacoco => https://lakshmidrip.github.io/DROP/jacoco/index.html
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
*
* You may obtain a copy of the License at
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
*
* See the License for the specific language governing permissions and
* limitations under the License.
*/
/**
* <i>R1CentralFisherProxy</i> implements the Univariate Normal Proxy Version using the Fisher Transformation
* for the R<sup>1</sup> Chi-Square Distribution. The References are:
*
* <br><br>
* <ul>
* <li>
* Abramowitz, M., and I. A. Stegun (2007): <i>Handbook of Mathematics Functions</i> <b>Dover Book
* on Mathematics</b>
* </li>
* <li>
* Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of
* Speech and Audio <i>IEEE/ACM Transactions on Audio, Speech, and Language Processing</i> <b>26
* (1)</b> 19-30
* </li>
* <li>
* Chi-Squared Distribution (2019): Chi-Squared Function
* https://en.wikipedia.org/wiki/Chi-squared_distribution
* </li>
* <li>
* Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): <i>Continuous Univariate Distributions
* 2<sup>nd</sup> Edition</i> <b>John Wiley and Sons</b>
* </li>
* <li>
* National Institute of Standards and Technology (2019): Chi-Squared Distribution
* https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm
* </li>
* </ul>
*
* <br><br>
* <ul>
* <li><b>Module </b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/ComputationalCore.md">Computational Core Module</a></li>
* <li><b>Library</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/NumericalAnalysisLibrary.md">Numerical Analysis Library</a></li>
* <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>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/measure/chisquare/README.md">Chi-Square Distribution Implementation/Properties</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class R1CentralFisherProxy extends org.drip.measure.continuous.R1Univariate
{
private int _degreesOfFreedom = -1;
private org.drip.measure.gaussian.R1UnivariateNormal _r1UnivariateNormal = null;
/**
* R1CentralFisherProxy Constructor
*
* @param degreesOfFreedom Degrees of Freedom
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public R1CentralFisherProxy (
final int degreesOfFreedom)
throws java.lang.Exception
{
if (0 >= (_degreesOfFreedom = degreesOfFreedom))
{
throw new java.lang.Exception ("R1CentralFisherProxy Constructor => Invalid Inputs");
}
_r1UnivariateNormal = new org.drip.measure.gaussian.R1UnivariateNormal (
java.lang.Math.sqrt (2. * _degreesOfFreedom - 1),
1.
);
}
/**
* Retrieve the Degrees of Freedom
*
* @return The Degrees of Freedom
*/
public int degreesOfFreedom()
{
return _degreesOfFreedom;
}
/**
* Retrieve the R^1 Univariate Normal
*
* @return The R^1 Univariate Normal
*/
public org.drip.measure.gaussian.R1UnivariateNormal r1UnivariateNormal()
{
return _r1UnivariateNormal;
}
@Override public double[] support()
{
return new double[]
{
0.,
java.lang.Double.POSITIVE_INFINITY
};
}
@Override public double density (
final double t)
throws java.lang.Exception
{
return _r1UnivariateNormal.density (t);
}
@Override public double cumulative (
final double t)
throws java.lang.Exception
{
return _r1UnivariateNormal.cumulative (t);
}
@Override public double mean()
throws java.lang.Exception
{
return _r1UnivariateNormal.mean();
}
@Override public double median()
throws java.lang.Exception
{
return _r1UnivariateNormal.median();
}
@Override public double mode()
throws java.lang.Exception
{
return _r1UnivariateNormal.mode();
}
@Override public double variance()
throws java.lang.Exception
{
return 1.;
}
@Override public double skewness()
throws java.lang.Exception
{
return _r1UnivariateNormal.skewness();
}
@Override public double excessKurtosis()
throws java.lang.Exception
{
return _r1UnivariateNormal.excessKurtosis();
}
@Override public double differentialEntropy()
throws java.lang.Exception
{
return _r1UnivariateNormal.differentialEntropy();
}
@Override public org.drip.function.definition.R1ToR1 momentGeneratingFunction()
{
return _r1UnivariateNormal.momentGeneratingFunction();
}
@Override public org.drip.function.definition.R1ToR1 probabilityGeneratingFunction()
{
return _r1UnivariateNormal.probabilityGeneratingFunction();
}
@Override public double random()
throws java.lang.Exception
{
double sumOfStandardNormalSquares = 0.;
for (int drawIndex = 0; drawIndex < _degreesOfFreedom; ++drawIndex)
{
double randomStandardNormal = org.drip.measure.gaussian.NormalQuadrature.InverseCDF
(java.lang.Math.random());
sumOfStandardNormalSquares = sumOfStandardNormalSquares +
randomStandardNormal * randomStandardNormal;
}
return java.lang.Math.sqrt (2. * sumOfStandardNormalSquares);
}
}