Generalised Gamma distribution (GG)

Density, distribution function, quantile function, and random generation for the generalised Gamma distribution.

Usage

dgengamma(x, mu = 1, sigma = 0.5, nu = 1, log = FALSE)

pgengamma(q, mu = 1, sigma = 0.5, nu = 1, lower.tail = TRUE, log.p = FALSE)

qgengamma(p, mu = 1, sigma = 0.5, nu = 1, lower.tail = TRUE, log.p = FALSE)

rgengamma(n, mu = 1, sigma = 0.5, nu = 1)

Arguments

x, q

vector of quantiles

mu

location parameter, must be positive.

sigma

scale parameter, must be positive.

nu

skewness parameter (real).

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

lower.tail

logical; if TRUE (default), probabilities are \(P[X \le x]\), otherwise \(P[X > x]\).

p

vector of probabilities

n

number of random values to return

Value

dgengamma gives the density, pgengamma gives the distribution function, qgengamma gives the quantile function, and rgengamma generates random deviates.

Details

This implementation of dgengamma, pgengamma, and qgengamma allows for automatic differentiation with RTMB.

References

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC, doi:10.1201/9780429298547. An older version can be found in https://www.gamlss.com/.

Examples

x <- rgengamma(5, mu = 4, sigma = 0.5, nu = 0.5)
d <- dgengamma(x, mu = 4, sigma = 0.5, nu = 0.5)
p <- pgengamma(x, mu = 4, sigma = 0.5, nu = 0.5)
q <- qgengamma(p, mu = 4, sigma = 0.5, nu = 0.5)