extraDistr (version 1.9.1)

InvChiSq: Inverse chi-squared and scaled chi-squared distributions

Description

Density, distribution function and random generation for the inverse chi-squared distribution and scaled chi-squared distribution.

Usage

dinvchisq(x, nu, tau, log = FALSE)
pinvchisq(q, nu, tau, lower.tail = TRUE, log.p = FALSE)
qinvchisq(p, nu, tau, lower.tail = TRUE, log.p = FALSE)
rinvchisq(n, nu, tau)

Arguments

x, q

vector of quantiles.

nu

positive valued shape parameter.

tau

positive valued scaling parameter; if provided it returns values for scaled chi-squared distributions.

log, log.p

logical; if TRUE, probabilities p are given 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 observations. If length(n) > 1, the length is taken to be the number required.

Details

If $X$ follows ${\chi }^2(\nu )$ distribution, then $1/X$ follows inverse chi-squared distribution parametrized by $\nu$. Inverse chi-squared distribution is a special case of inverse gamma distribution with parameters $\alpha =\frac{\nu }{2}$ and $\beta =\frac{1}{2}$; or $\alpha =\frac{\nu }{2}$ and $\beta =\frac{\nu {\tau }^2}{2}$ for scaled inverse chi-squared distribution.

See Also

Chisquare, GammaDist

Examples

x <- rinvchisq(1e5, 20)
hist(x, 100, freq = FALSE)
curve(dinvchisq(x, 20), 0, 1, n = 501, col = "red", add = TRUE)
hist(pinvchisq(x, 20))
plot(ecdf(x))
curve(pinvchisq(x, 20), 0, 1, n = 501, col = "red", lwd = 2, add = TRUE)

# scaled

x <- rinvchisq(1e5, 10, 5)
hist(x, 100, freq = FALSE)
curve(dinvchisq(x, 10, 5), 0, 150, n = 501, col = "red", add = TRUE)
hist(pinvchisq(x, 10, 5))
plot(ecdf(x))
curve(pinvchisq(x, 10, 5), 0, 150, n = 501, col = "red", lwd = 2, add = TRUE)