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Reparameterised beta distribution

beta2.Rd

Density, distribution function, quantile function, and random generation for the beta distribution reparameterised in terms of mean and concentration.

Usage

dbeta(x, shape1, shape2, log = FALSE, eps = 0)

dbeta2(x, mu, phi, log = FALSE, eps = 0)

pbeta2(q, mu, phi, lower.tail = TRUE, log.p = FALSE)

qbeta2(p, mu, phi, lower.tail = TRUE, log.p = FALSE)

rbeta2(n, mu, phi)

Arguments

x, q

vector of quantiles

shape1, shape2

non-negative parameters

log, log.p

logical; if TRUE, probabilities/ densities \(p\) are returned as \(\log(p)\).

eps

for internal use only, don't change.

mu

mean parameter, must be in the interval from 0 to 1.

phi

concentration parameter, must be positive.

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.

Value

dbeta2 gives the density, pbeta2 gives the distribution function, qbeta2 gives the quantile function, and rbeta2 generates random deviates.

Details

This implementation allows for automatic differentiation with RTMB.

Currently, dbeta masks RTMB::dbeta because the latter has a numerically unstable gradient.

Examples

set.seed(123)
x <- rbeta2(1, 0.5, 1)
d <- dbeta2(x, 0.5, 1)
p <- pbeta2(x, 0.5, 1)
q <- qbeta2(p, 0.5, 1)