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

In VGAM: Vector Generalized Linear and Additive Models

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.
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.

Details

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

Value

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

Author(s)

T. W. Yee and Kai Huang

See Also

lino.

Examples

## 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 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

## End(Not run)

VGAM documentation built on Sept. 18, 2024, 9:09 a.m.