betaprime: Beta prime distribution

In RTMBdist: Distributions Compatible with Automatic Differentiation by 'RTMB'

Beta prime distribution

Description

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

Usage

dbetaprime(x, shape1, shape2, log = FALSE)

pbetaprime(q, shape1, shape2, lower.tail = TRUE, log.p = FALSE)

qbetaprime(p, shape1, shape2, lower.tail = TRUE, log.p = FALSE)

rbetaprime(n, shape1, shape2)

Arguments

x, q	vector of quantiles
shape1, shape2	non-negative shape parameters of the corresponding Beta distribution
log, log.p	logical; if TRUE, probabilities/ densities p are returned 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 random values to return.

Details

This implementation allows for automatic differentiation with RTMB.

If X \sim \text{Beta}(\alpha, \beta), then \frac{X}{1-X} \sim \text{Betaprime}(\alpha, \beta)

Value

dbetaprime gives the density, pbetaprime gives the distribution function, qbetaprime gives the quantile function, and rbetaprime generates random deviates.

Examples

x <- rbetaprime(1, 2, 1)
d <- dbetaprime(x, 2, 1)
p <- pbetaprime(x, 2, 1)
q <- qbetaprime(p, 2, 1)

RTMBdist documentation built on April 1, 2026, 5:07 p.m.