invchisq: Inverse Chi-squared distribution

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

Inverse Chi-squared distribution

Description

Density, distribution function, quantile function, and random generation for the inverse Chi-squared distribution.

Usage

dinvchisq(x, df, scale = 1/df, log = FALSE)

pinvchisq(q, df, scale = 1/df, lower.tail = TRUE, log.p = FALSE)

qinvchisq(p, df, scale = 1/df, lower.tail = TRUE, log.p = FALSE)

rinvchisq(n, df, scale = 1/df)

Arguments

x, q	vector of quantiles, must be positive.
df	degrees of freedom (\nu > 0)
scale	optional positive scale parameter. Default value of 1/df corresponds to standard inverse gamma
log, log.p	logical; if TRUE, probabilities/densities 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

If X \sim \text{Chisq}(\nu), then 1/X \sim \text{invChisq}(\nu).

The inverse Chi-squared distribution with \nu degrees of freedom has density

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

This implementation of dinvchisq, pinvchisq, and qinvchisq allows for automatic differentiation with RTMB.

Value

dinvchisq gives the density, pinvchisq gives the distribution function, qinvchisq gives the quantile function, and rinvchisq generates random deviates.

Examples

x <- rinvchisq(1, df = 5)
d <- dinvchisq(x, df = 5)
p <- pinvchisq(x, df = 5)
q <- qinvchisq(p, df = 5)

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