# InvChiSq: Inverse chi-squared and scaled chi-squared distributions In extraDistr: Additional Univariate and Multivariate Distributions

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```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 ≤ 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 χ^2 (ν) distribution, then 1/X follows inverse chi-squared distribution parametrized by ν. Inverse chi-squared distribution is a special case of inverse gamma distribution with parameters α=ν/2 and β=1/2; or α=ν/2 and β=(ντ^2)/2 for scaled inverse chi-squared distribution.

`Chisquare`, `GammaDist`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```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) ```