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, log=FALSE)
    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`.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### 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 0.7-9 Index]