The Generalized Beta Distribution (Libby and Novick, 1982)
Density, distribution function, quantile function and random generation for the generalized beta distribution, as proposed by Libby and Novick (1982).
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)
See lino, the VGAM family function
for estimating the parameters,
for the formula of the probability density function and other details.
dlino gives the density,
plino gives the distribution function,
qlino gives the quantile function, and
rlino generates random deviates.
T. W. Yee and Kai Huang
lino.
## 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
## End(Not run)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.