Package org.drip.measure.gamma

Class ErlangDistribution

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.gamma.R1ShapeScaleDistribution

org.drip.measure.gamma.ErlangDistribution

public class ErlangDistribution
extends R1ShapeScaleDistribution

ErlangDistribution implements the Shape and Scale Parameterization of the R¹ Erlang 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

Constructor Summary

Constructors

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

Method Summary

Modifier and Type	Method	Description
double	cumulative(double x)	Compute the cumulative under the distribution to the given value
double	waitingTime()	Compute the kth Arrival Poisson Waiting Time

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

bannehekeEkayanakeMedianApproximation, chenRubinMedianLowerBound, chenRubinMedianUpperBound, cltProxy, 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, random, randomArray, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object

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

Constructor Details

ErlangDistribution

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

ErlangDistribution Constructor

Parameters:

shapeParameter - Shape Parameter

scaleParameter - Scale Parameter

gammaEstimator - Gamma Estimator

digammaEstimator - Digamma Estimator

lowerIncompleteGammaEstimator - Lower Incomplete Gamma Estimator

Throws:

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

Method Details

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 R1ShapeScaleDistribution

Parameters:

x - Variate to which the cumulative is to be computed

Returns:

The cumulative

Throws:

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

waitingTime

public double waitingTime()

Compute the k^th Arrival Poisson Waiting Time

Returns:

The k^th Arrival Poisson Waiting Time