BetaPrime: Beta prime distribution

In twolodzko/extraDistr: Additional Univariate and Multivariate Distributions

Beta prime distribution

Description

Density, distribution function, quantile function and random generation for the beta prime distribution.

Usage

dbetapr(x, shape1, shape2, scale = 1, log = FALSE)

pbetapr(q, shape1, shape2, scale = 1, lower.tail = TRUE, log.p = FALSE)

qbetapr(p, shape1, shape2, scale = 1, lower.tail = TRUE, log.p = FALSE)

rbetapr(n, shape1, shape2, scale = 1)

Arguments

x, q	vector of quantiles.
shape1, shape2	non-negative parameters.
scale	positive valued scale parameter.
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

If X \sim \mathrm{Beta}(\alpha, \beta), then \frac{X}{1-X} \sim \mathrm{BetaPrime}(\alpha, \beta).

Probability density function

f(x) = \frac{(x/\sigma)^{\alpha-1} (1+x/\sigma)^{-\alpha -\beta}}{\mathrm{B}(\alpha,\beta)\sigma}

Cumulative distribution function

F(x) = I_{\frac{x/\sigma}{1+x/\sigma}}(\alpha, \beta)

See Also

Beta

Examples

x <- rbetapr(1e5, 5, 3, 2)
hist(x, 350, freq = FALSE, xlim = c(0, 100))
curve(dbetapr(x, 5, 3, 2), 0, 100, col = "red", add = TRUE, n = 500)
hist(pbetapr(x, 5, 3, 2))
plot(ecdf(x), xlim = c(0, 100))
curve(pbetapr(x, 5, 3, 2), 0, 100, col = "red", add = TRUE, n = 500)

twolodzko/extraDistr documentation built on Dec. 4, 2023, 8:56 p.m.