R1ShapeScaleGammaMGF

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.measure.generators.R1MomentGeneratingFunction

org.drip.measure.generators.R1ShapeScaleGammaMGF

public class R1ShapeScaleGammaMGF
extends R1MomentGeneratingFunction

R1ShapeScaleGammaMGF implements the Shape/Scale Parametrized Gamma Distribution R1ToR1 Moment Generating Function. 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

It provides the following Functionality:

R1ShapeScaleGammaMGF Constructor
Evaluate the Moment Generating Function at t

Module	Computational Core Module
Library	Numerical Analysis Library
Project	R^d Continuous/Discrete Probability Measures
Package	R¹/R^d Moment/Probability Generating Functions

Author:: Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor Description

R1ShapeScaleGammaMGF(R1ShapeScaleDistribution r1GammaDistribution)
R1ShapeScaleGammaMGF Constructor
Method Summary

Modifier and Type Method Description

double evaluate(double t)
Evaluate the Moment Generating Function at t

Methods inherited from class org.drip.measure.generators.R1MomentGeneratingFunction
distribution

Methods inherited from class org.drip.function.definition.R1ToR1
antiDerivative, conditionNumber, derivative, differential, differential, integrate, maxima, maxima, minima, minima, poleResidue

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

Constructor Details
- R1ShapeScaleGammaMGF
  
  public R1ShapeScaleGammaMGF(R1ShapeScaleDistribution r1GammaDistribution) throws java.lang.Exception
  
  R1ShapeScaleGammaMGF Constructor
  
  Parameters:
  
  r1GammaDistribution - Underlying R¹ Rate Parametrized Gamma Distribution
  
  Throws:
  
  java.lang.Exception - Thrown if the Inputs are Invalid
Method Details
- evaluate
  
  public double evaluate(double t) throws java.lang.Exception
  
  Evaluate the Moment Generating Function at t
  
  Overrides:
  
  evaluate in class R1MomentGeneratingFunction
  
  Parameters:
  
  t - MGF "t"
  
  Returns:
  
  Moment Generating Function evaluated at t
  
  Throws:
  
  java.lang.Exception - Thrown if the Moment Generating Function cannot be evaluated