# invchisq: The Inverse (non-central) Chi-Squared Distribution In dkahle/invgamma: The Inverse Gamma Distribution

## Description

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

## Usage

 ```1 2 3 4 5 6 7``` ```dinvchisq(x, df, ncp = 0, log = FALSE) pinvchisq(q, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) qinvchisq(p, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) rinvchisq(n, df, ncp = 0) ```

## Arguments

 `x, q` vector of quantiles. `df` degrees of freedom (non-negative, but can be non-integer). `ncp` non-centrality parameter (non-negative). `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

The functions (d/p/q/r)invchisq simply wrap those of the standard (d/p/q/r)chisq R implementation, so look at, say, `dchisq` for details.

`dchisq`; these functions just wrap the (d/p/q/r)chisq functions.
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```s <- seq(0, 3, .01) plot(s, dinvchisq(s, 3), type = 'l') f <- function(x) dinvchisq(x, 3) q <- 2 integrate(f, 0, q) (p <- pinvchisq(q, 3)) qinvchisq(p, 3) # = q mean(rinvchisq(1e5, 3) <= q) f <- function(x) dinvchisq(x, 3, ncp = 2) q <- 1.5 integrate(f, 0, q) (p <- pinvchisq(q, 3, ncp = 2)) qinvchisq(p, 3, ncp = 2) # = q mean(rinvchisq(1e7, 3, ncp = 2) <= q) ```