Package org.drip.measure.exponential

Class R1ScaledDistribution

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.exponential.R1ScaledDistribution

public class R1ScaledDistribution
extends R1Univariate

R1ScaledDistribution implements the Probability Density Function for the Scaled R¹ Exponential 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

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d Continuous/Discrete Probability Measures
• Package = R¹ and R^d Continuous Random Measure

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1ScaledDistribution(ScaledExponentialEstimator scaledExponentialEstimator, R1ToR1 gammaEstimator)	R1ScaledDistribution Constructor

Method Summary

Modifier and Type	Method	Description
double	cumulative(double t)	Compute the cumulative under the distribution to the given value
double	density(double t)	Compute the Density under the Distribution at the given Variate
R1ToR1	gammaEstimator()	Retrieve the Gamma Estimator
double	incremental(double t1, double t2)	Compute the Incremental under the Distribution between the 2 variates
double	lambda()	Retrieve the "Lambda" Parameter
double	mean()	Retrieve the Mean of the Distribution
double	normalizer()	Retrieve the Normalizer
ScaledExponentialEstimator	scaledExponentialEstimator()	Retrieve the Scaled Exponential Estimator
double[]	support()	Lay out the Support of the PDF Range
double	variance()	Retrieve the Variance of the Distribution

Methods inherited from class org.drip.measure.continuous.R1Univariate

bPOE, centralMoment, cvar, differentialEntropy, excessKurtosis, expectedShortfall, fisherInformation, histogram, invCumulative, iqr, kullbackLeiblerDivergence, median, mode, momentGeneratingFunction, nonCentralMoment, populationCentralMeasures, probabilityGeneratingFunction, quantile, random, randomArray, skewness, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Constructor Details

R1ScaledDistribution

public R1ScaledDistribution(ScaledExponentialEstimator scaledExponentialEstimator,
R1ToR1 gammaEstimator)
                     throws java.lang.Exception

R1ScaledDistribution Constructor

Parameters:

scaledExponentialEstimator - Scaled Exponential Estimator

gammaEstimator - Gamma Estimator

Throws:

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

Method Details

scaledExponentialEstimator

public ScaledExponentialEstimator scaledExponentialEstimator()

Retrieve the Scaled Exponential Estimator

Returns:

Scaled Exponential Estimator

gammaEstimator

public R1ToR1 gammaEstimator()

Retrieve the Gamma Estimator

Returns:

Gamma Estimator

support

public double[] support()

Description copied from class: R1Univariate

Lay out the Support of the PDF Range

Specified by:

support in class R1Univariate

Returns:

Support of the PDF Range

density

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

Description copied from class: R1Univariate

Compute the Density under the Distribution at the given Variate

Specified by:

density in class R1Univariate

Parameters:

t - Variate at which the Density needs to be computed

Returns:

The Density

Throws:

java.lang.Exception - Thrown if the input is invalid

cumulative

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

Description copied from class: R1Univariate

Compute the cumulative under the distribution to the given value

Specified by:

cumulative in class R1Univariate

Parameters:

t - Variate to which the cumulative is to be computed

Returns:

The cumulative

Throws:

java.lang.Exception - Thrown if the inputs are invalid

incremental

public double incremental(double t1,
double t2)
                   throws java.lang.Exception

Description copied from class: R1Univariate

Compute the Incremental under the Distribution between the 2 variates

Overrides:

incremental in class R1Univariate

Parameters:

t1 - Left Variate to which the cumulative is to be computed

t2 - Right Variate to which the cumulative is to be computed

Returns:

The Incremental under the Distribution between the 2 variates

Throws:

java.lang.Exception - Thrown if the inputs are invalid

mean

public double mean()
            throws java.lang.Exception

Description copied from class: R1Univariate

Retrieve the Mean of the Distribution

Specified by:

mean in class R1Univariate

Returns:

The Mean of the Distribution

Throws:

java.lang.Exception - Thrown if the Mean cannot be estimated

variance

public double variance()
                throws java.lang.Exception

Description copied from class: R1Univariate

Retrieve the Variance of the Distribution

Specified by:

variance in class R1Univariate

Returns:

The Variance of the Distribution

Throws:

java.lang.Exception - Thrown if the Variance cannot be estimated

normalizer

public double normalizer()

Retrieve the Normalizer

Returns:

Normalizer

lambda

public double lambda()

Retrieve the "Lambda" Parameter

Returns:

"Lambda" Parameter