RTMBdist (version 1.0.1)

beta2: Reparameterised beta distribution

Description

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)

Value

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

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.

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)