invgamma: Inverse Gamma distribution

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

Inverse Gamma distribution

Description

Density, distribution function, and random generation for the inverse Gamma distribution.

Usage

dinvgamma(x, shape, rate, scale = 1/rate, log = FALSE)

pinvgamma(q, shape, rate, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)

qinvgamma(p, shape, rate, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)

rinvgamma(n, shape, rate, scale = 1/rate)

Arguments

x, q	vector of quantiles, must be positive.
shape, rate, scale	positive parameters of corresponding gamma distribution
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 of dinvgamma, pinvgamma, and qinvgamma allows for automatic differentiation with RTMB.

If X \sim \Gamma(\alpha, \beta), then 1/X \sim \text{InvGamma}(\alpha, \beta).

Value

dinvgamma gives the density, pinvgamma gives the distribution function, qinvgamma gives the quantile function, and rinvgamma generates random deviates.

Examples

x <- rinvgamma(1, 1, 0.5)
d <- dinvgamma(x, 1, 0.5)
p <- pinvgamma(x, 1, 0.5)
q <- qinvgamma(p, 1, 0.5)

RTMBdist documentation built on April 1, 2026, 5:07 p.m.