Package org.drip.measure.chisquare

Class R1NonCentralCumulantInvariant

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.chisquare.R1NonCentral

org.drip.measure.chisquare.R1NonCentralCumulantInvariant

public class R1NonCentralCumulantInvariant
extends R1NonCentral

R1NonCentralCumulantInvariant implements the Cumulant Invariant Transformation 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

Constructor Summary

Constructors

Constructor	Description
R1NonCentralCumulantInvariant(R1NonCentralParameters r1NonCentralParameters, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator, double sankaranB)	R1NonCentralCumulantInvariant Constructor

Method Summary

Modifier and Type	Method	Description
double	cumulative(double x)	Compute the cumulative under the distribution to the given value
double	density(double x)	Compute the Density under the Distribution at the given Variate
static R1NonCentralCumulantInvariant	InvariantFourthCumulant(int degreesOfFreedom, double nonCentralityParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	Construct the Fourth Cumulant Invariant Instance of R1NonCentralCumulantInvariant
static R1NonCentralCumulantInvariant	InvariantSecondCumulant(int degreesOfFreedom, double nonCentralityParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	Construct the Second Cumulant Invariant Instance of R1NonCentralCumulantInvariant
static R1NonCentralCumulantInvariant	InvariantThirdCumulant(int degreesOfFreedom, double nonCentralityParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)	Construct the Third Cumulant Invariant Instance of R1NonCentralCumulantInvariant
double	invCumulative(double y)	Compute the inverse cumulative under the distribution corresponding to the given value
double	sankaranB()	Retrieve the Sankaran (1963) "B"

Methods inherited from class org.drip.measure.chisquare.R1NonCentral

cumulant, digammaEstimator, excessKurtosis, gammaEstimator, leadingCentralMoments, leadingRawMoments, lowerIncompleteGammaEstimator, mean, modifiedBesselFirstKindEstimator, momentGeneratingFunction, nonCentralMoment, parameters, skewness, Standard, support, variance

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

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

Methods inherited from class java.lang.Object

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

Constructor Details

R1NonCentralCumulantInvariant

public R1NonCentralCumulantInvariant(R1NonCentralParameters r1NonCentralParameters,
R1ToR1 gammaEstimator,
R1ToR1 digammaEstimator,
R2ToR1 lowerIncompleteGammaEstimator,
ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator,
double sankaranB)
                              throws java.lang.Exception

R1NonCentralCumulantInvariant Constructor

Parameters:

r1NonCentralParameters - R¹ Non-central Parameters

gammaEstimator - Gamma Estimator

digammaEstimator - Digamma Estimator

lowerIncompleteGammaEstimator - Lower Incomplete Gamma Estimator

modifiedBesselFirstKindEstimator - Modified Bessel First Kind Estimator

sankaranB - Sankaran (1963) "B"

Throws:

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

Method Details

InvariantSecondCumulant

public static final R1NonCentralCumulantInvariant InvariantSecondCumulant(int degreesOfFreedom,
double nonCentralityParameter,
R1ToR1 gammaEstimator,
R1ToR1 digammaEstimator,
R2ToR1 lowerIncompleteGammaEstimator,
ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)

Construct the Second Cumulant Invariant Instance of R1NonCentralCumulantInvariant

Parameters:

degreesOfFreedom - Degrees of Freedom

nonCentralityParameter - Non-centrality Parameter

gammaEstimator - Gamma Estimator

digammaEstimator - Digamma Estimator

lowerIncompleteGammaEstimator - Lower Incomplete Gamma Estimator

modifiedBesselFirstKindEstimator - Modified Bessel First Kind Estimator

Returns:

The Second Cumulant Invariant Instance of R1NonCentralCumulantInvariant

InvariantThirdCumulant

public static final R1NonCentralCumulantInvariant InvariantThirdCumulant(int degreesOfFreedom,
double nonCentralityParameter,
R1ToR1 gammaEstimator,
R1ToR1 digammaEstimator,
R2ToR1 lowerIncompleteGammaEstimator,
ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)

Construct the Third Cumulant Invariant Instance of R1NonCentralCumulantInvariant

Parameters:

degreesOfFreedom - Degrees of Freedom

nonCentralityParameter - Non-centrality Parameter

gammaEstimator - Gamma Estimator

digammaEstimator - Digamma Estimator

lowerIncompleteGammaEstimator - Lower Incomplete Gamma Estimator

modifiedBesselFirstKindEstimator - Modified Bessel First Kind Estimator

Returns:

The Third Cumulant Invariant Instance of R1NonCentralCumulantInvariant

InvariantFourthCumulant

public static final R1NonCentralCumulantInvariant InvariantFourthCumulant(int degreesOfFreedom,
double nonCentralityParameter,
R1ToR1 gammaEstimator,
R1ToR1 digammaEstimator,
R2ToR1 lowerIncompleteGammaEstimator,
ModifiedBesselFirstKindEstimator modifiedBesselFirstKindEstimator)

Construct the Fourth Cumulant Invariant Instance of R1NonCentralCumulantInvariant

Parameters:

degreesOfFreedom - Degrees of Freedom

nonCentralityParameter - Non-centrality Parameter

gammaEstimator - Gamma Estimator

digammaEstimator - Digamma Estimator

lowerIncompleteGammaEstimator - Lower Incomplete Gamma Estimator

modifiedBesselFirstKindEstimator - Modified Bessel First Kind Estimator

Returns:

The Fourth Cumulant Invariant Instance of R1NonCentralCumulantInvariant

sankaranB

public double sankaranB()

Retrieve the Sankaran (1963) "B"

Returns:

Sankaran (1963) "B"

density

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

Description copied from class: R1Univariate

Compute the Density under the Distribution at the given Variate

Overrides:

density in class R1NonCentral

Parameters:

x - 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 x)
                  throws java.lang.Exception

Description copied from class: R1Univariate

Compute the cumulative under the distribution to the given value

Overrides:

cumulative in class R1NonCentral

Parameters:

x - Variate to which the cumulative is to be computed

Returns:

The cumulative

Throws:

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

invCumulative

public double invCumulative(double y)
                     throws java.lang.Exception

Description copied from class: R1Univariate

Compute the inverse cumulative under the distribution corresponding to the given value

Overrides:

invCumulative in class R1Univariate

Parameters:

y - Value corresponding to which the inverse cumulative is to be computed

Returns:

The inverse cumulative

Throws:

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