betagen: The Generalised Beta Distribution

In mc2d: Tools for Two-Dimensional Monte-Carlo Simulations

The Generalised Beta Distribution

Description

Density, distribution function, quantile function and random generation for the Beta distribution defined on the ‘⁠[min, max]⁠’ domain with parameters ‘⁠shape1⁠’ and ‘⁠shape2⁠’ ( and optional non-centrality parameter ‘⁠ncp⁠’).

Usage

dbetagen(x, shape1, shape2, min=0, max=1, ncp=0, log=FALSE)
pbetagen(q, shape1, shape2, min=0, max=1, ncp=0, lower.tail=TRUE,
	  log.p=FALSE)
qbetagen(p, shape1, shape2, min=0, max=1, ncp=0, lower.tail=TRUE,
	  log.p=FALSE)
rbetagen(n, shape1, shape2, min=0, max=1, ncp=0)

Arguments

x,q	Vector of quantiles.
p	Vector of probabilities.
n	Number of observations. If ‘⁠length(n) > 1⁠’, the length is taken to be the number required.
shape1, shape2	Positive parameters of the Beta distribution.
min	Vector of minima.
max	Vector of maxima.
ncp	Non-centrality parameter of the Beta distribution.
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]⁠’.

Details

x \sim betagen(shape1, shape2, min, max, ncp)

if

\frac{x-min}{max-min}\sim beta(shape1,shape2,ncp)

These functions use the Beta distribution functions after correct parameterization.

Value

‘⁠dbetagen⁠’ gives the density, ‘⁠pbetagen⁠’ gives the distribution function, ‘⁠qbetagen⁠’ gives the quantile function, and ‘⁠rbetagen⁠’ generates random deviates.

See Also

Beta

Examples

curve(dbetagen(x, shape1=3, shape2=5, min=1, max=6), from = 0, to = 7)
curve(dbetagen(x, shape1=1, shape2=1, min=2, max=5), from = 0, to = 7, lty=2, add=TRUE)
curve(dbetagen(x, shape1=.5, shape2=.5, min=0, max=7), from = 0, to = 7, lty=3, add=TRUE)

mc2d documentation built on July 26, 2023, 6:07 p.m.