BetaPrime function

Beta prime distribution

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

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 $X ~ Beta(\alpha, \beta)$, then $X/(1-X) ~ BetaPrime(\alpha, \beta)$.

Probability density function

Cumulative distribution function

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)

See Also

Beta