sbeta {skewunit}R Documentation

The symmetrical beta distribution.

Description

Density, distribution function and random generation for the symmetrical beta distribution.

Usage

dsbeta(x, delta=1, log=FALSE)
psbeta(q, delta=1, lower.tail=TRUE, log.p=FALSE)
rsbeta(n, delta=1)

Arguments

x, q

vector of quantiles.

n

number of observations. If length(n) > 1, the length is taken to be the number required.

delta

shape parameter (by default is 1).

log, log.p

logical; if TRUE, probabilities p are given as log(p).

lower.tail

logical; if TRUE (default), probabilities are P[X\leq x], otherwise, P[X>x].

Details

The symmetrical beta distribution has density

f(x)=\frac{1}{B(\delta,\delta)}x^{\delta-1}(1-x)^{\delta-1}, \quad x \in (0,1), \delta>0,

where B(a,b) denotes the beta function. Its cumulative distribution function is

F(x)=I_x(\delta,\delta), \quad x \in (0,1).

Value

dsbeta gives the density, psbeta gives the distribution function, and rsbeta generates random deviates. The length of the result is determined by n for rasin, and is the maximum of the lengths of the numerical arguments for the other functions. The numerical arguments other than n are recycled to the length of the result. Only the first elements of the logical arguments are used.

Author(s)

Diego Gallardo

Examples

dsbeta(0.5, 1.2)
psbeta(0.5, 0.5)
rsbeta(5, 1.5)

[Package skewunit version 1.0 Index]