RelaxationTimeDistributionEstimator.java
package org.drip.specialfunction.definition;
/*
* -*- 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>RelaxationTimeDistributionEstimator</i> exposes the Estimator for the Relaxation Time Distribution
* Function. The References are:
*
* <br><br>
* <ul>
* <li>
* Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015):
* <i>Tables of Integrals, Series, and Products</i> <b>Academic Press</b>
* </li>
* <li>
* Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye
* Susceptibilities in Glassy Systems <i>Physical Review E</i> <b>65 (6)</b> 061510
* </li>
* <li>
* Wikipedia (2019): Stretched Exponential Function
* https://en.wikipedia.org/wiki/Stretched_exponential_function
* </li>
* <li>
* Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic
* Error-Bounds, Double Exponential Transform, and Open Source Implementation <i>libkw</i>
* <i>Algorithm</i> <b>5 (4)</b> 604-628
* </li>
* <li>
* Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions <i>Journal of Chemical
* Physics</i> <b>116 (8)</b> 3204-3209
* </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/FunctionAnalysisLibrary.md">Function Analysis Library</a></li>
* <li><b>Project</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/README.md">Special Function Implementation Analysis</a></li>
* <li><b>Package</b> = <a href = "https://github.com/lakshmiDRIP/DROP/tree/master/src/main/java/org/drip/specialfunction/definition/README.md">Definition of Special Function Estimators</a></li>
* </ul>
*
* @author Lakshmi Krishnamurthy
*/
public abstract class RelaxationTimeDistributionEstimator extends org.drip.function.definition.R1ToR1
{
protected RelaxationTimeDistributionEstimator()
{
super (null);
}
/**
* Compute the Relaxation Time Density
*
* @param t Time Instant
*
* @return The Relaxation Time Density
*
* @throws java.lang.Exception Thrown if the Inputs are Invalid
*/
abstract public double relaxationTimeDensity (
final double t)
throws java.lang.Exception;
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
return relaxationTimeDensity (t);
}
/**
* Construct the G Function Version
*
* @return The G Function Version
*/
public org.drip.function.definition.R1ToR1 gFunction()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
return t * relaxationTimeDensity (t);
}
};
}
/**
* Construct the G Function for beta = 0.5
*
* @return The G Function for beta = 0.5
*/
public static final org.drip.function.definition.R1ToR1 GFunctionHalfBeta()
{
return new org.drip.function.definition.R1ToR1 (null)
{
@Override public double evaluate (
final double t)
throws java.lang.Exception
{
return 0.5 * java.lang.Math.sqrt (t / java.lang.Math.PI) *
java.lang.Math.exp (-0.25 * t);
}
};
}
}