Package org.drip.measure.generators

Class R1CentralChiSquaredMGF

java.lang.Object

org.drip.function.definition.R1ToR1

org.drip.measure.generators.R1MomentGeneratingFunction

org.drip.measure.generators.R1CentralChiSquaredMGF

public class R1CentralChiSquaredMGF
extends R1MomentGeneratingFunction

R1CentralChiSquaredMGF implements the Central Chi-squared R1ToR1 Moment Generating Function. The References are:

• Abramowitz, M., and I. A. Stegun (2007): Handbook of Mathematics Functions Dover Book on Mathematics
• Backstrom, T., and J. Fischer (2018): Fast Randomization for Distributed Low Bit-rate Coding of Speech and Audio IEEE/ACM Transactions on Audio, Speech, and Language Processing 26 (1) 19-30
• Chi-Squared Distribution (2019): Chi-Squared Function https://en.wikipedia.org/wiki/Chi-squared_distribution
• Johnson, N. L., S. Kotz, and N. Balakrishnan (1994): Continuous Univariate Distributions 2^nd Edition John Wiley and Sons
• National Institute of Standards and Technology (2019): Chi-Squared Distribution https://www.itl.nist.gov/div898/handbook/eda/section3/eda3666.htm

It provides the following Functionality:

• R1CentralChiSquaredMGF Constructor
• Evaluate the Moment Generating Function at t

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

Author:

Lakshmi Krishnamurthy

Constructor Summary

Constructors

Constructor	Description
R1CentralChiSquaredMGF(R1Central r1CentralChiSquaredDistribution)	R1CentralChiSquaredMGF 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

R1CentralChiSquaredMGF

public R1CentralChiSquaredMGF(R1Central r1CentralChiSquaredDistribution)
                       throws java.lang.Exception

R1CentralChiSquaredMGF Constructor

Parameters:

r1CentralChiSquaredDistribution - Underlying R¹ Central Chi-squared 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