Lino {VGAM}R Documentation

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)
plino(q, shape1, shape2, lambda=1)
qlino(p, shape1, shape2, lambda=1)
rlino(n, shape1, shape2, lambda=1)

Arguments

x, q vector of quantiles.
p vector of probabilities.
n number of observations. Must be a positive integer of length 1.
shape1, shape2, lambda see lino.

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

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 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)

[Package VGAM version 0.7-7 Index]