ConjugateShapeScalePrior.java
package org.drip.measure.gamma;
/*
* -*- 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>ConjugateShapeScalePrior</i> implements the Determinants of the Parameters of the Conjugate Prior for
* the Shape and the Scale Parameters. The References are:
*
* <br><br>
* <ul>
* <li>
* Devroye, L. (1986): <i>Non-Uniform Random Variate Generation</i> <b>Springer-Verlag</b> New York
* </li>
* <li>
* Gamma Distribution (2019): Gamma Distribution
* https://en.wikipedia.org/wiki/Chi-squared_distribution
* </li>
* <li>
* Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the
* Gamma Distribution Derived From Likelihood Equations <i>The American Statistician</i> <b>73
* (2)</b> 195-199
* </li>
* <li>
* Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
* </li>
* <li>
* Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from
* Likelihood Equations <i>The American Statistician</i> <b>71 (2)</b> 177-181
* </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/gamma/README.md">R<sup>1</sup> Gamma Distribution Implementation/Properties</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public class ConjugateShapeScalePrior
{
private org.drip.function.definition.R1ToR1 _gammaEstimator = null;
private org.drip.measure.gamma.ConjugateScalePrior _conjugateScalePrior = null;
private org.drip.measure.gamma.ConjugateShapePrior _conjugateShapePrior = null;
/**
* ConjugateShapeScalePrior Constructor
*
* @param conjugateShapePrior The Conjugate Shape Prior
* @param conjugateScalePrior The Conjugate Scale Prior
* @param gammaEstimator The Gamma Estimator
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public ConjugateShapeScalePrior (
final org.drip.measure.gamma.ConjugateShapePrior conjugateShapePrior,
final org.drip.measure.gamma.ConjugateScalePrior conjugateScalePrior,
final org.drip.function.definition.R1ToR1 gammaEstimator)
throws java.lang.Exception
{
if (null == (_conjugateShapePrior = conjugateShapePrior) ||
null == (_conjugateScalePrior = conjugateScalePrior) ||
null == (_gammaEstimator = gammaEstimator)
)
{
throw new java.lang.Exception (
"ConjugateShapeScalePrior Constructor => Invalid Inputs"
);
}
}
/**
* Retrieve the Conjugate Shape Prior
*
* @return The Conjugate Shape Prior
*/
public org.drip.measure.gamma.ConjugateShapePrior conjugateShapePrior()
{
return _conjugateShapePrior;
}
/**
* Retrieve the Conjugate Scale Prior
*
* @return The Conjugate Scale Prior
*/
public org.drip.measure.gamma.ConjugateScalePrior conjugateScalePrior()
{
return _conjugateScalePrior;
}
/**
* Retrieve the Gamma Estimator
*
* @return Gamma Estimator
*/
public org.drip.function.definition.R1ToR1 gammaEstimator()
{
return _gammaEstimator;
}
/**
* Compute the Conjugate Shape-Scale Unnormalized Prior Probability
*
* @return The Conjugate Shape-Scale Unnormalized Prior Probability
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
public double unnormalizedPriorProbability()
throws java.lang.Exception
{
double scaleEstimate = _conjugateScalePrior.parameterEstimate();
double shapeEstimate = _conjugateShapePrior.parameterEstimate();
return java.lang.Math.pow (
_conjugateShapePrior.observationProduct(),
shapeEstimate - 1.
) * java.lang.Math.exp (
-1. * _conjugateScalePrior.observationSum() / scaleEstimate
) * java.lang.Math.pow (
_gammaEstimator.evaluate (
shapeEstimate
),
-1. * _conjugateShapePrior.observationCount()
) * java.lang.Math.pow (
scaleEstimate,
-1. * shapeEstimate * _conjugateScalePrior.observationCount()
);
}
/**
* Perform an Bayes' Update of the Conjugate Prior from the Sample
*
* @param sample The Sample
*
* @return TRUE - Bayes' Update of the Conjugate Prior from the Sample completed successfully
*/
public boolean bayesUpdate (
final org.drip.validation.evidence.Sample sample)
{
return _conjugateScalePrior.bayesUpdate (
sample
) && _conjugateShapePrior.bayesUpdate (
sample
);
}
}