# R/invchi.R In chi: The Chi Distribution

#### Documented in dinvchipinvchiqinvchirinvchi

```#' The Inverse Chi Distribution
#'
#' Density, distribution function, quantile function and random
#' generation for the inverse chi distribution.
#'
#' @param x,q vector of quantiles.
#' @param p vector of probabilities.
#' @param n number of observations. If length(n) > 1, the length is
#'   taken to be the number required.
#' @param df degrees of freedom (non-negative, but can be
#'   non-integer).
#' @param ncp non-centrality parameter (non-negative).
#' @param log,log.p logical; if TRUE, probabilities p are given as
#'   log(p).
#' @param lower.tail logical; if TRUE (default), probabilities are
#'   P[X <= x] otherwise, P[X > x].
#' @seealso \code{\link{dchi}}
#' @name invchi
#' @examples
#'
#' s <- seq(0, 2, .01)
#' plot(s, dinvchi(s, 7), type = 'l')
#'
#' f <- function(x) dinvchi(x, 7)
#' q <- .5
#' integrate(f, 0, q)
#' (p <- pinvchi(q, 7))
#' qinvchi(p, 7) # = q
#' mean(rinvchi(1e5, 7) <= q)
#'
#'
#' samples <- rinvchi(1e5, 7)
#' plot(density(samples))
#' curve(f, add = TRUE, col = "red")
#'
#'
NULL

#' @rdname invchi
#' @export
dinvchi <- function(x, df, ncp = 0, log = FALSE) {
log_f <- dchi(1/x, df, ncp, log = TRUE) - 2*log(x)
if(log) return(log_f)
exp(log_f)
}

#' @rdname invchi
#' @export
pinvchi <- function(q, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) {
pchi(1/q, df, ncp, !lower.tail, log.p)
}

#' @rdname invchi
#' @export
qinvchi <- function(p, df, ncp = 0, lower.tail = TRUE, log.p = FALSE) {
qchi(1-p, df, ncp, lower.tail, log.p)^(-1)
}

#' @rdname invchi
#' @export
rinvchi <- function(n, df, ncp = 0) {
1 / rchi(n, df, ncp)
}
```

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chi documentation built on May 30, 2017, 5:19 a.m.