ACDm (version 1.0.3)

dgenf: The generalized F distribution

Description

Density and distribution function for the generalized F distribution. Warning: the distribution function pgenf and genfHazard are computed numerically, and may not be precise!

Usage

dgenf(x, kappa = 5, eta = 1.5, gamma = .8, lambda = 1, forceExpectation = F)
pgenf(q, kappa = 5, eta = 1.5, gamma = .8, lambda = 1, forceExpectation = F)
genfHazard(x, kappa = 5, eta = 1.5, gamma = .8, lambda = 1, forceExpectation = F)

Arguments

x, q

vector of quantiles.

kappa, eta, gamma, lambda

parameters, see 'Details'.

forceExpectation

logical; if TRUE, the expectation of the distribution is forced to be 1 by letting theta be a function of the other parameters.

Details

The PDF for the generelized F distribution is: $$f(\epsilon)= \frac{\gamma \epsilon^{\kappa \gamma -1}[\eta+(\epsilon/\lambda)^{\gamma}]^{-\eta-\kappa}\eta^{\eta}}{\lambda^{\kappa \gamma}B(\kappa,\eta)},$$ where $B(\kappa,\eta)=\frac{\Gamma(\kappa)\Gamma(\eta)}{\Gamma(\kappa+\eta)}$ is the beta function.