InvChiSq function

Inverse chi-squared and scaled chi-squared distributions

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

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 $\alpha=\nu/2$ and $\beta=1/2$; or $\alpha=\nu/2$ and $\beta=(\nu\tau^2)/2$ for scaled inverse chi-squared distribution.

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)

See Also

Chisquare, GammaDist