Package org.drip.measure.chisquare

Class R1CentralWilsonHilferty

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.chisquare.R1WilsonHilferty

org.drip.measure.chisquare.R1CentralWilsonHilferty

public class R1CentralWilsonHilferty
extends R1WilsonHilferty

R1CentralWilsonHilferty implements the Normal Proxy Version for the R¹ Chi-Square Distribution using the Wilson-Hilferty Transfomation. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of Speech and Audio IEEE/ACM Transactions on Audio, Speech, and Language Processing 26 (1) 19-30
• Chi-Squared Distribution (2019): Chi-Squared Function https://en.wikipedia.org/wiki/Chi-squared_distribution
• Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions 2^nd Edition John Wiley and Sons
• National Institute of Standards and Technology (2019): Chi-Squared Distribution https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

• 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	inverseTransform(double wilsonHilferty)	Transform the Wilson-Hilferty Variate into x
double	random()	Generate a Random Variable corresponding to the Distribution
static R1CentralWilsonHilferty	Standard(int degreesOfFreedom)	Construct a Standard Instance of R1CentralWilsonHilferty
double	transform(double x)	Transform x into the Wilson-Hilferty Variate

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, 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 R1CentralWilsonHilferty Standard(int degreesOfFreedom)

Construct a Standard Instance of R1CentralWilsonHilferty

Parameters:

degreesOfFreedom - Degrees of Freedom

Returns:

Standard Instance of R1CentralWilsonHilferty

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

random

public double random()
              throws java.lang.Exception

Description copied from class: R1Univariate

Generate a Random Variable corresponding to the Distribution

Overrides:

random in class R1Univariate

Returns:

Random Variable corresponding to the Distribution

Throws:

java.lang.Exception - Thrown if the Random Instance cannot be estimated