R1GammaToExponential

java.lang.Object

org.drip.measure.continuous.R1Univariate

org.drip.measure.gamma.R1ShapeScaleDistribution

org.drip.measure.transform.R1GammaToExponential

public class R1GammaToExponential
extends R1ShapeScaleDistribution

R1GammaToExponential implements the R¹ Exponential Distribution in Terms 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

Constructor Summary

Constructors
Constructor	Description
`R1GammaToExponential(double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator)`	R1GammaToExponential Constructor

Method Summary

Modifier and Type Method Description

R1ShapeScaleDistribution iidDistribution(int n)
Construct a Gamma Distribution Based of n i.i.d.

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, random, randomArray, supported, tukeyAnomaly, tukeyCriterion

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Details
- R1GammaToExponential
  
  public R1GammaToExponential(double scaleParameter, R1ToR1 gammaEstimator, R1ToR1 digammaEstimator, R2ToR1 lowerIncompleteGammaEstimator) throws java.lang.Exception
  
  R1GammaToExponential Constructor
  
  Parameters:
  
  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
- iidDistribution
  
  public R1ShapeScaleDistribution iidDistribution(int n)
  
  Construct a Gamma Distribution Based of n i.i.d. Exponential Distributions
  
  Parameters:
  
  n - n
  
  Returns:
  
  The Gamma Distribution