gamma2: Reparameterised gamma distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Reparameterised gamma distribution

Description

Density, distribution function, quantile function, and random generation for the gamma distribution reparameterised in terms of mean and standard deviation.

Usage

dgamma2(x, mean = 1, sd = 1, log = FALSE)

pgamma2(q, mean = 1, sd = 1, lower.tail = TRUE, log.p = FALSE)

qgamma2(p, mean = 1, sd = 1, lower.tail = TRUE, log.p = FALSE)

rgamma2(n, mean = 1, sd = 1)

Arguments

x, q	vector of quantiles
mean	mean parameter, must be positive.
sd	standard deviation parameter, must be positive.
log, log.p	logical; if TRUE, probabilities/ densities p are returned as \log(p).
lower.tail	logical; if TRUE, probabilities are P[X \le x], otherwise, P[X > x].
p	vector of probabilities
n	number of random values to return.

Details

This implementation allows for automatic differentiation with RTMB.

Reparameterises the gamma distribution via \text{shape} = \mu^2/s^2 and \text{scale} = s^2/\mu:

f(x;\,\mu, s) = \frac{x^{\mu^2/s^2 - 1} \exp(-x s^2/\mu^2)}{(s^2/\mu)^{\mu^2/s^2}\,\Gamma(\mu^2/s^2)}, \quad x > 0.

Value

dgamma2 gives the density, pgamma2 gives the distribution function, qgamma2 gives the quantile function, and rgamma2 generates random deviates.

Examples

x <- rgamma2(1)
d <- dgamma2(x)
p <- pgamma2(x)
q <- qgamma2(p)

RTMBdist documentation built on Oct. 31, 2026, 5:07 p.m.