Inverse-gamma distribution
Density, distribution function and random generation for the inverse-gamma distribution.
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)
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 ≤ x] otherwise, P[X > x]. |
p |
vector of probabilities. |
n |
number of observations. If |
Probability mass function
f(x) = (β^α * x^(-α-1) * exp(-β/x)) / Γ(α)
Cumulative distribution function
F(x) = γ(α, β/x) / Γ(α)
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.
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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.