betagen: The Generalised Beta Distribution

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

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 ~ betagen(shape1, shape2, min, max, ncp)

if

(x-min)/(max-min)~beta(shape1,shape2,ncp)

These functions use the Beta distribution functions after correct parametrisation.

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 5, 2021, 3:01 p.m.