BetaPrime: Beta prime distribution

Description Usage Arguments Details See Also Examples

Description

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

Usage

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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 ≤ 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 ~ Beta(α, β), then X/(1-X) ~ BetaPrime(α, β).

Probability density function

f(x) = ((x/σ)^(α-1) * (1 + x/σ)^(-α-β)) / (B(α,β) * σ)

Cumulative distribution function

F(x) = pbeta((x/σ)/(1+(x/σ)), α, β)

See Also

Beta

Examples

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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)

extraDistr documentation built on Sept. 7, 2020, 5:09 p.m.