Benini {VGAM} | R Documentation

## The Benini Distribution

### Description

Density, distribution function, quantile function and random generation for the Benini distribution with parameter `shape`.

### Usage

    dbenini(x, shape, y0, log=FALSE)
    pbenini(q, shape, y0)
    qbenini(p, shape, y0)
    rbenini(n, shape, y0)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Must be a positive integer of length 1.
`shape` | the shape parameter b.
`y0` | the scale parameter y0.
`log` | Logical. If `log=TRUE` then the logarithm of the density is returned.

### Details

See `benini`, the VGAM family function for estimating the parameter b by maximum likelihood estimation, for the formula of the probability density function and other details.

### Value

`dbenini` gives the density, `pbenini` gives the distribution function, `qbenini` gives the quantile function, and `rbenini` generates random deviates.

### Author(s)

T. W. Yee

### References

Kleiber, C. and Kotz, S. (2003) Statistical Size Distributions in Economics and Actuarial Sciences, Hoboken, NJ: Wiley-Interscience.

### See Also

`benini`.

### Examples

    ## Not run:
    y0 = 1
    shape = exp(1)
    x = seq(-0.0, 4, len=101)
    plot(x, dbenini(x, y0=y0,shape=shape), type="l", col="blue", las=1,
         main="Blue is density, red is cumulative distribution function",
         sub="Purple lines are the 10,20,...,90 percentiles", ylim=0:1,
         ylab="")
    abline(h=0, col="blue", lty=2)
    lines(x, pbenini(x, y0=y0,shape=shape), col="red")
    probs = seq(0.1, 0.9, by=0.1)
    Q = qbenini(probs, y0=y0,shape=shape)
    lines(Q, dbenini(Q, y0=y0,shape=shape), col="purple", lty=3, type="h")
    pbenini(Q, y0=y0,shape=shape) - probs    # Should be all zero
    ## End(Not run)

[Package VGAM version 0.7-9 Index]