Beta                  package:base                  R Documentation

The Beta Distribution

Description:

     Density, distribution function, quantile function and random
     generation for the Beta distribution with parameters `shape1' and
     `shape2' (and optional non-centrality parameter `ncp').

Usage:

     dbeta(x, shape1, shape2, ncp=0, log = FALSE)
     pbeta(q, shape1, shape2, ncp=0, lower.tail = TRUE, log.p = FALSE)
     qbeta(p, shape1, shape2,        lower.tail = TRUE, log.p = FALSE)
     rbeta(n, shape1, shape2)

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.

     ncp: non-centrality parameter.

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:

     The Beta distribution with parameters `shape1' = a and `shape2' =
     b has density

           Gamma(a+b)/(Gamma(a)Gamma(b))x^(a-1)(1-x)^(b-1)

     for a > 0, b > 0 and 0 < x < 1.

Value:

     `dbeta' gives the density, `pbeta' the distribution function,
     `qbeta' the quantile function, and `rbeta' generates random
     deviates.

See Also:

     `beta' for the Beta function, and `dgamma' for the Gamma
     distribution.

Examples:

     x <- seq(0, 1, length=21)
     dbeta(x, 1, 1)
     pbeta(x, 1, 1)

