# GeneralizedGammaDist: The generelized Gamma distribution In ACDm: Tools for Autoregressive Conditional Duration Models

## 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.

### Details

The PDF for the generelized Gamma distribution is:

f(x)=\frac{γ x^{κ γ - 1}}{λ^{κ γ}Γ (κ)}\exp ≤ft\{{-≤ft(\frac{x}{λ}\right)^{γ}}\right\}

### 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.

### Author(s)

Markus Belfrage

ACDm documentation built on Nov. 16, 2022, 5:09 p.m.