VGAM (version 1.1-8)

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)

Value

dlino gives the density,

plino gives the distribution function,

qlino gives the quantile function, and

rlino generates random deviates.

Arguments

x, q

vector of quantiles.

p

vector of probabilities.

n

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.

Author

T. W. Yee and Kai Huang

Details

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

See Also

lino.

Examples

if (FALSE)   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 PDF, orange is the CDF",
     sub = "Purple lines are the 10,20,...,90 percentiles")
abline(h = 0, col = "blue", lty = 2)
lines(x, plino(x, shape1, shape2, lambda = lambda), col = "orange")
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, shape2, lambda = lambda) - probs  # Should be all 0