R1RateGammaMGF

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.measure.generators.R1MomentGeneratingFunction

org.drip.measure.generators.R1RateGammaMGF

public class R1RateGammaMGF
extends R1MomentGeneratingFunction

R1RateGammaMGF implements the Rate Parametrized Gamma Distribution R1ToR1 Moment Generating Function. The References are:

Devroye, L. (1986): Non-Uniform Random Variate Generation Springer-Verlag New York
Exponential Distribution (2019): Exponential Distribution https://en.wikipedia.org/wiki/Exponential_distribution
Norton, M., V. Khokhlov, and S. Uryasev (2019): Calculating CVaR and bPOE for Common Probability Distributions with Application to Portfolio Optimization and Density Estimation Annals of Operations Research 299 (1-2) 1281-1315
Ross, S. M. (2009): Introduction to Probability and Statistics for Engineers and Scientists 4^th Edition Associated Press New York, NY
Schmidt, D. F., and D. Makalic (2009): Universal Models for the Exponential Distribution IEEE Transactions on Information Theory 55 (7) 3087-3090

It provides the following Functionality:

R1RateGammaMGF 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

R1RateGammaMGF(R1RateDistribution r1GammaDistribution)
R1RateGammaMGF 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
- R1RateGammaMGF
  
  public R1RateGammaMGF(R1RateDistribution r1GammaDistribution) throws java.lang.Exception
  
  R1RateGammaMGF 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