contextual (version 0.9.8.4)

invgamma: The Inverse Gamma Distribution

Description

Density, distribution function, quantile function and random generation for the inverse gamma distribution.

Usage

dinvgamma(x, shape, rate = 1, scale = 1/rate, log = FALSE)
pinvgamma(q, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
qinvgamma(p, shape, rate = 1, scale = 1/rate, lower.tail = TRUE, log.p = FALSE)
rinvgamma(n, shape, rate = 1, scale = 1/rate)

Arguments

x, q

vector of quantiles.

shape

inverse gamma shape parameter

rate

inverse gamma rate parameter

scale

alternative to rate; scale = 1/rate

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 inverse gamma distribution with parameters shape and rate has density f(x) = rate^shape/Gamma(shape) x^(-1-shape) e^(-rate/x) it is the inverse of the standard gamma parameterization in R.

The functions (d/p/q/r)invgamma simply wrap those of the standard (d/p/q/r)gamma R implementation, so look at, say, dgamma for details.

Examples

# NOT RUN {
s <- seq(0, 5, .01)
plot(s, dinvgamma(s, 7, 10), type = 'l')

f <- function(x) dinvgamma(x, 7, 10)
q <- 2
integrate(f, 0, q)
(p <- pinvgamma(q, 7, 10))
qinvgamma(p, 7, 10) # = q
mean(rinvgamma(1e5, 7, 10) <= q)
# }