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The Inverse (non-central) Chi-Squared Distribution

Source: R/invchisq.R
invchisq.Rd

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

Usage

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 \(P[X \leq x]\); if FALSE \(P[X > x]\).

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, stats::dchisq() for details.

See also

stats::dchisq(); these functions just wrap the (d/p/q/r)chisq() functions.

Examples


s <- seq(0, 3, .01)
plot(s, dinvchisq(s, 3), type = 'l')


f <- function(x) dinvchisq(x, 3)
q <- 2
integrate(f, 0, q)
#> 0.9188914 with absolute error < 9.4e-07
(p <- pinvchisq(q, 3))
#> [1] 0.9188914
qinvchisq(p, 3) # = q
#> [1] 2
mean(rinvchisq(1e5, 3) <= q)
#> [1] 0.91924




f <- function(x) dinvchisq(x, 3, ncp = 2)
q <- 1.5
integrate(f, 0, q)
#> 0.950349 with absolute error < 3.8e-06
(p <- pinvchisq(q, 3, ncp = 2))
#> [1] 0.950349
qinvchisq(p, 3, ncp = 2) # = q
#> [1] 1.5
mean(rinvchisq(1e7, 3, ncp = 2) <= q)
#> [1] 0.9502991