The 4-Parameter Beta Distribution in Regression Parameterization

Density, distribution function, quantile function, and random generation for the 4-parameter beta distribution in regression parameterization.

Usage

dbeta4(x, mu, phi, theta1 = 0, theta2 = 1 - theta1, log = FALSE)

pbeta4(q, mu, phi, theta1 = 0, theta2 = 1 - theta1, lower.tail = TRUE, log.p = FALSE)

qbeta4(p, mu, phi, theta1 = 0, theta2 = 1 - theta1, lower.tail = TRUE, log.p = FALSE)

rbeta4(n, mu, phi, theta1 = 0, theta2 = 1 - theta1)

Arguments

x, q

numeric. Vector of quantiles.

p

numeric. Vector of probabilities.

n

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

mu

numeric. The mean of the beta distribution that is extended to support [theta1, theta2].

phi

numeric. The precision parameter of the beta distribution that is extended to support [theta1, theta2].

theta1, theta2

numeric. The minimum and maximum, respectively, of the 4-parameter beta distribution. By default a symmetric support is chosen by theta2 = 1 - theta1 which reduces to the classic beta distribution because of the default theta1 = 0.

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 distribution is obtained by a linear transformation of a beta-distributed random variable with intercept theta1 and slope theta2 - theta1.

Value

dbeta4 gives the density, pbeta4 gives the distribution function, qbeta4 gives the quantile function, and rbeta4 generates random deviates.

See also

dbetar, Beta4