Inverse Chi-squared distribution — invchisq • RTMBdist

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

Value

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

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.

Examples

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