InvGamma: Inverse-gamma distribution

In extraDistr: Additional Univariate and Multivariate Distributions

Inverse-gamma distribution

Description

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

Usage

dinvgamma(x, alpha, beta = 1, log = FALSE)

pinvgamma(q, alpha, beta = 1, lower.tail = TRUE, log.p = FALSE)

qinvgamma(p, alpha, beta = 1, lower.tail = TRUE, log.p = FALSE)

rinvgamma(n, alpha, beta = 1)

Arguments

x, q	vector of quantiles.
alpha, beta	positive valued shape and scale parameters.
log, log.p	logical; if TRUE, probabilities p are given as log(p).
lower.tail	logical; if TRUE (default), probabilities are P[X \le 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

Probability mass function

f(x) = \frac{\beta^\alpha x^{-\alpha-1} \exp(-\frac{\beta}{x})}{\Gamma(\alpha)}

Cumulative distribution function

F(x) = \frac{\gamma(\alpha, \frac{\beta}{x})}{\Gamma(\alpha)}

References

Witkovsky, V. (2001). Computing the distribution of a linear combination of inverted gamma variables. Kybernetika 37(1), 79-90.

Leemis, L.M. and McQueston, L.T. (2008). Univariate Distribution Relationships. American Statistician 62(1): 45-53.

See Also

GammaDist

Examples

x <- rinvgamma(1e5, 20, 3)
hist(x, 100, freq = FALSE)
curve(dinvgamma(x, 20, 3), 0, 1, col = "red", add = TRUE, n = 5000)
hist(pinvgamma(x, 20, 3))
plot(ecdf(x))
curve(pinvgamma(x, 20, 3), 0, 1, col = "red", lwd = 2, add = TRUE, n = 5000) 

extraDistr documentation built on May 29, 2024, 9:31 a.m.