Package org.drip.specialfunction.definition

Class RelaxationTimeDistributionEstimator

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.specialfunction.definition.RelaxationTimeDistributionEstimator

Direct Known Subclasses:

RelaxationTimeDistributionSeriesEstimator

public abstract class RelaxationTimeDistributionEstimator
extends R1ToR1

RelaxationTimeDistributionEstimator exposes the Estimator for the Relaxation Time Distribution Function. The References are:

• Gradshteyn, I. S., I. M. Ryzhik, Y. V. Geronimus, M. Y. Tseytlin, and A. Jeffrey (2015): Tables of Integrals, Series, and Products Academic Press
• Hilfer, J. (2002): H-function Representations for Stretched Exponential Relaxation and non-Debye Susceptibilities in Glassy Systems Physical Review E 65 (6) 061510
• Wikipedia (2019): Stretched Exponential Function https://en.wikipedia.org/wiki/Stretched_exponential_function
• Wuttke, J. (2012): Laplace-Fourier Transform of the Stretched Exponential Function: Analytic Error-Bounds, Double Exponential Transform, and Open Source Implementation libkw Algorithm 5 (4) 604-628
• Zorn, R. (2002): Logarithmic Moments of Relaxation Time Distributions Journal of Chemical Physics 116 (8) 3204-3209

It provides the following functionality:

• Construct the Relaxation Time Density
• Construct the G Function Version
• Construct the G Function for beta = 0.5

Module	Product Core Module
Library	Fixed Income Analytics
Project	Special Function Implementation and Analysis
Package	Definition of Special Function Estimators

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	evaluate(double t)	Evaluate for the given variate
R1ToR1	gFunction()	Construct the G Function Version
static R1ToR1	GFunctionHalfBeta()	Construct the G Function for beta = 0.5
abstract double	relaxationTimeDensity(double t)	Compute the Relaxation Time Density

Methods inherited from class org.drip.function.definition.R1ToR1

antiDerivative, derivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Method Details

relaxationTimeDensity

public abstract double relaxationTimeDensity(double t)
                                      throws java.lang.Exception

Compute the Relaxation Time Density

Parameters:

t - Time Instant

Returns:

The Relaxation Time Density

Throws:

java.lang.Exception - Thrown if the Inputs are Invalid

evaluate

public double evaluate(double t)
                throws java.lang.Exception

Description copied from class: R1ToR1

Evaluate for the given variate

Specified by:

evaluate in class R1ToR1

Parameters:

t - Variate

Returns:

Returns the calculated value

Throws:

java.lang.Exception - Thrown if evaluation cannot be done

gFunction

public R1ToR1 gFunction()

Construct the G Function Version

Returns:

The G Function Version

GFunctionHalfBeta

public static final R1ToR1 GFunctionHalfBeta()

Construct the G Function for beta = 0.5

Returns:

The G Function for beta = 0.5