Package org.drip.measure.chisquare

Class R1NonCentralAbdelAty

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.chisquare.R1WilsonHilferty

org.drip.measure.chisquare.R1NonCentralWilsonHaferty

org.drip.measure.chisquare.R1NonCentralAbdelAty

public class R1NonCentralAbdelAty
extends R1NonCentralWilsonHaferty

R1NonCentralAbdelAty implements the Abdel-Aty (1954) Wilson-Haferty Approximation for the R¹ Non-central Chi-Square Distribution. The References are:

• Johnson, N. L., S. Kotz, and N. Balakrishnan (1995): Continuous Univariate Distributions 2^nd Edition John Wiley and Sons
• Muirhead, R. (2005): Aspects of Multivariate Statistical Theory 2^nd Edition Wiley
• Non-central Chi-Squared Distribution (2019): Chi-Squared Function https://en.wikipedia.org/wiki/Noncentral_chi-squared_distribution
• Sankaran, M. (1963): Approximations to the Non-Central Chi-Square Distribution Biometrika 50 (1-2) 199-204
• Young, D. S. (2010): tolerance: An R Package for Estimating Tolerance Intervals Journal of Statistical Software 36 (5) 1-39

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d Continuous/Discrete Probability Measures
• Package = Chi-Square Distribution Implementation/Properties

Author:

Lakshmi Krishnamurthy

Method Summary

Modifier and Type	Method	Description
double	f()	Retrieve the Abdel-Aty (1954) f Parameter
double	inverseTransform(double wilsonHilferty)	Transform the Wilson-Hilferty Variate into x
static R1NonCentralAbdelAty	Standard(int degreesOfFreedom, double nonCentralityParameter)	Construct a Standard Instance of R1NonCentralAbdelAty
double	transform(double x)	Transform x into the Wilson-Hilferty Variate

Methods inherited from class org.drip.measure.chisquare.R1NonCentralWilsonHaferty

parameters

Methods inherited from class org.drip.measure.chisquare.R1WilsonHilferty

cumulative, degreesOfFreedom, density, excessKurtosis, invCumulative, mean, median, mode, momentGeneratingFunction, probabilityGeneratingFunction, r1UnivariateNormal, skewness, support, variance

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

bPOE, centralMoment, cvar, differentialEntropy, expectedShortfall, fisherInformation, histogram, incremental, iqr, kullbackLeiblerDivergence, nonCentralMoment, populationCentralMeasures, quantile, random, randomArray, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Method Details

Standard

public static final R1NonCentralAbdelAty Standard(int degreesOfFreedom,
double nonCentralityParameter)

Construct a Standard Instance of R1NonCentralAbdelAty

Parameters:

degreesOfFreedom - Degrees of Freedom

nonCentralityParameter - Non-centrality Parameter

Returns:

Standard Instance of R1NonCentralAbdelAty

f

public double f()

Retrieve the Abdel-Aty (1954) f Parameter

Returns:

The Abdel-Aty (1954) f Parameter

transform

public double transform(double x)

Description copied from class: R1WilsonHilferty

Transform x into the Wilson-Hilferty Variate

Specified by:

transform in class R1WilsonHilferty

Parameters:

x - X

Returns:

The Wilson-Hilferty Variate

inverseTransform

public double inverseTransform(double wilsonHilferty)

Description copied from class: R1WilsonHilferty

Transform the Wilson-Hilferty Variate into x

Specified by:

inverseTransform in class R1WilsonHilferty

Parameters:

wilsonHilferty - The Wilson-Hilferty Variate

Returns:

The Wilson-Hilferty Variate transformed back to x