ACDm (version 1.0.3)

GeneralizedGammaDist: The generelized Gamma distribution

Description

Density (PDF), distribution function (CDF), quantile function (inverted CDF), random generation and hazard function for the generelized Gamma distribution with parameters gamma, kappa and lambda.

Usage

dgengamma(x, gamma = 0.3, kappa = 1.2, lambda = 0.3, forceExpectation = F)
pgengamma(x, gamma = .3, kappa = 3, lambda = .3, forceExpectation = F)
qgengamma(p, gamma = .3, kappa = 3, lambda = .3, forceExpectation = F)
rgengamma(n = 1, gamma = .3, kappa = 3, lambda = .3, forceExpectation = F)
gengammaHazard(x, gamma = .3, kappa = 3, lambda = .3, forceExpectation = F)

Arguments

x

vector of quantiles.

p

vector of probabilities.

n

number of observations..

gamma, kappa, 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.

Value

• dgengamma gives the density (PDF), pgengamma gives the distribution function (CDF), qgengamma gives the quantile function (inverted CDF), rgenGamma generates random deviates, and genGammaHazard gives the hazard function.

Details

The PDF for the generelized Gamma distribution is: $$f(x)=\frac{\gamma x^{\kappa \gamma - 1}}{\lambda^{\kappa \gamma}\Gamma (\kappa)}\exp \left{{-\left(\frac{x}{\lambda}\right)^{\gamma}}\right}$$