Lino: The Generalized Beta Distribution (Libby and Novick, 1982)

Description

Density, distribution function, quantile function and random generation for the generalized beta distribution, as proposed by Libby and Novick (1982).

Usage

dlino(x, shape1, shape2, lambda = 1, log = FALSE)
plino(q, shape1, shape2, lambda = 1, lower.tail = TRUE, log.p = FALSE)
qlino(p, shape1, shape2, lambda = 1, lower.tail = TRUE, log.p = FALSE)
rlino(n, shape1, shape2, lambda = 1)

Arguments

x, q

vector of quantiles.

vector of probabilities.

number of observations. Same as in runif.

shape1, shape2, lambda

see lino.

log

Logical. If log = TRUE then the logarithm of the density is returned.

lower.tail, log.p

Same meaning as in pnorm or qnorm.

Value

dlino gives the density, plino gives the distribution function, qlino gives the quantile function, and rlino generates random deviates.

Details

See lino, the VGAM family function for estimating the parameters, for the formula of the probability density function and other details.

Examples

Run this code

# NOT RUN {
lambda <- 0.4; shape1 <- exp(1.3); shape2 <- exp(1.3)
x <- seq(0.0, 1.0, len = 101)
plot(x, dlino(x, shape1 = shape1, shape2 = shape2, lambda = lambda),
     type = "l", col = "blue", las = 1, ylab = "",
     main = "Blue is density, red is cumulative distribution function",
     sub = "Purple lines are the 10,20,...,90 percentiles")
abline(h = 0, col = "blue", lty = 2)
lines(x, plino(x, shape1 = shape1, shape2 = shape2, l = lambda), col = "red")
probs <- seq(0.1, 0.9, by = 0.1)
Q <- qlino(probs, shape1 = shape1, shape2 = shape2, lambda = lambda)
lines(Q, dlino(Q, shape1 = shape1, shape2 = shape2, lambda = lambda),
      col = "purple", lty = 3, type = "h")
plino(Q, shape1 = shape1, shape2 = shape2, l = lambda) - probs  # Should be all 0
# }