Package org.drip.measure.gamma

Class R1ShapeScaleDiscrete

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.gamma.R1ShapeScaleDistribution

org.drip.measure.gamma.R1ShapeScaleDiscrete

public class R1ShapeScaleDiscrete
extends R1ShapeScaleDistribution

R1ShapeScaleDiscrete generates Discrete Variables that are Derivatives of the R¹ Gamma Distribution. The References are:

• Devroye, L. (1986): Non-Uniform Random Variate Generation Springer-Verlag New York
• Gamma Distribution (2019): Gamma Distribution https://en.wikipedia.org/wiki/Chi-squared_distribution
• Louzada, F., P. L. Ramos, and E. Ramos (2019): A Note on Bias of Closed-Form Estimators for the Gamma Distribution Derived From Likelihood Equations The American Statistician 73 (2) 195-199
• Minka, T. (2002): Estimating a Gamma distribution https://tminka.github.io/papers/minka-gamma.pdf
• Ye, Z. S., and N. Chen (2017): Closed-Form Estimators for the Gamma Distribution Derived from Likelihood Equations The American Statistician 71 (2) 177-181

• Module = Computational Core Module
• Library = Numerical Analysis Library
• Project = R^d Continuous/Discrete Probability Measures
• Package = R¹ Gamma Distribution Implementation/Properties

Author:

Lakshmi Krishnamurthy

Field Summary

Fields

Modifier and Type	Field	Description
static int	DISCRETE_RANDOM_FROM_AHRENS_DIETER	Generate Random Discrete from Ahrens-Dieter (1982) Scheme
static int	DISCRETE_RANDOM_FROM_INVERSE_CDF	Generate Random Discrete from Inverse CDF
static int	DISCRETE_RANDOM_FROM_MARSAGLIA	Generate Random Discrete from Marsaglia (1977) Scheme

Constructor Summary

Constructors

Constructor	Description
R1ShapeScaleDiscrete(double shapeParameter, double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator, int randomGenerationScheme)	R1ShapeScaleDiscrete Constructor

Method Summary

Modifier and Type	Method	Description
double	random()	Generate a Random Variable corresponding to the Distribution
double	randomGeneralizedGamma(double q)	Generate Generalized Gamma Distributed Random Number
int	randomGenerationScheme()	Retrieve the Discrete Random Number Generator Scheme
double	randomInverseGamma()	Generate Inverse Gamma Distributed Random Number

Methods inherited from class org.drip.measure.gamma.R1ShapeScaleDistribution

bannehekeEkayanakeMedianApproximation, chenRubinMedianLowerBound, chenRubinMedianUpperBound, cltProxy, cumulative, density, differentialEntropy, digammaEstimator, excessKurtosis, exponentialFamilyRepresentation, gammaEstimator, laplacian, logarithmicExpectation, lowerIncompleteGammaEstimator, mean, mode, momentGeneratingFunction, naturalParameters, naturalStatistics, ramanujanChoiMedianApproximation, randomAhrensDieter1982, randomMarsaglia1977, scale, ShapeRate, shapeScaleParameters, ShapeSummation, skewness, Standard, support, variance

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

bPOE, centralMoment, cvar, expectedShortfall, fisherInformation, histogram, incremental, invCumulative, iqr, kullbackLeiblerDivergence, median, nonCentralMoment, populationCentralMeasures, probabilityGeneratingFunction, quantile, randomArray, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Field Details

DISCRETE_RANDOM_FROM_INVERSE_CDF

public static final int DISCRETE_RANDOM_FROM_INVERSE_CDF

Generate Random Discrete from Inverse CDF

See Also:

Constant Field Values

DISCRETE_RANDOM_FROM_AHRENS_DIETER

public static final int DISCRETE_RANDOM_FROM_AHRENS_DIETER

Generate Random Discrete from Ahrens-Dieter (1982) Scheme

See Also:

Constant Field Values

DISCRETE_RANDOM_FROM_MARSAGLIA

public static final int DISCRETE_RANDOM_FROM_MARSAGLIA

Generate Random Discrete from Marsaglia (1977) Scheme

See Also:

Constant Field Values

Constructor Details

R1ShapeScaleDiscrete

public R1ShapeScaleDiscrete(double shapeParameter,
double scaleParameter,
R1ToR1 gammaEstimator,
R1ToR1 digammaEstimator,
R2ToR1 lowerIncompleteGammaEstimator,
int randomGenerationScheme)
                     throws java.lang.Exception

R1ShapeScaleDiscrete Constructor

Parameters:

shapeParameter - Shape Parameter

scaleParameter - Scale Parameter

gammaEstimator - Gamma Estimator

digammaEstimator - Digamma Estimator

lowerIncompleteGammaEstimator - Lower Incomplete Gamma Estimator

randomGenerationScheme - Scheme for the Random Gamma NUmber Generator

Throws:

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

Method Details

randomGenerationScheme

public int randomGenerationScheme()

Retrieve the Discrete Random Number Generator Scheme

Returns:

The Discrete Random Number Generator Scheme

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

randomGeneralizedGamma

public double randomGeneralizedGamma(double q)
                              throws java.lang.Exception

Generate Generalized Gamma Distributed Random Number

Parameters:

q - The Power Parameter

Returns:

The Generalized Gamma Distributed Random Number

Throws:

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

randomInverseGamma

public double randomInverseGamma()
                          throws java.lang.Exception

Generate Inverse Gamma Distributed Random Number

Returns:

The Generalized Gamma Distributed Random Number

Throws:

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