Beta {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 to generate.
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)
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