GGamma: Generalised Gamma Curve constructor function

In gestate: Generalised Survival Trial Assessment Tool Environment

Generalised Gamma Curve constructor function

Description

This creates a Curve object for a Generalised Gamma distribution.
Curve objects contain all necessary information to describe a distribution, including functions and parameters describing it.
See Details for information on parameterisation.

Usage

GGamma(theta, eta, rho)

Arguments

theta	Scale parameter for Generalised Gamma distribution.
eta	Shape parameter for Generalised Gamma distribution.
rho	Family parameter for Generalised Gamma distribution.

Details

The Generalised Gamma distribution has parameterisation:
f(x) = (rho x^((rho eta)-1) e^(-(x/theta)^rho) theta^(-rho eta) )/Gamma(eta)
F(x) = LPGamma(eta,(x/theta)^rho)/Gamma(eta)
where Gamma is the gamma function, and LPGamma is the lower partial gamma function.
As of v1.4.0, all values of eta are now fully supported.

Author(s)

Jasmin Ruehl

References

Tadikamalla PR, Random Sampling from the Generalized Gamma Distribution. Computing, 1979, 23(2), 199-203.

Examples

GGamma(theta=20,eta=2,rho=0.7)

gestate documentation built on April 26, 2023, 5:10 p.m.