Frechet {VGAM} | R Documentation

## The Frechet Distribution

### Description

Density, distribution function, quantile function and random generation for the three parameter Frechet distribution.

### Usage

    dfrechet(x, location=0, scale=1, shape, log=FALSE)
    pfrechet(q, location=0, scale=1, shape)
    qfrechet(p, location=0, scale=1, shape)
    rfrechet(n, location=0, scale=1, shape)

### Arguments

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

### Details

See `frechet2` and `frechet3`, the VGAM family functions for estimating the 2 (without location parameter) and 3 parameters by maximum likelihood estimation, for the formula of the probability density function and range restrictions on the parameters.

### Value

`dfrechet` gives the density, `pfrechet` gives the distribution function, `qfrechet` gives the quantile function, and `rfrechet` generates random deviates.

### Author(s)

T. W. Yee

### References

Castillo, E., Hadi, A. S., Balakrishnan, N. Sarabia, J. S. (2005) Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, N.J.: Wiley-Interscience.

### See Also

`frechet2`, `frechet3`.

### Examples

    ## Not run:
    shape = 5
    x = seq(-0.1, 3.5, len=100)
    plot(x, dfrechet(x, shape=shape), type="l", ylab="", las=1,
         main="Frechet density divided into 10 equal areas; red=cdf")
    abline(h=0, col="blue", lty=2)
    qq = qfrechet(seq(0.1,0.9,by=0.1), shape=shape)
    lines(qq, dfrechet(qq, shape=shape), col="purple", lty=3, type="h")
    lines(x, pfrechet(q=x, shape=shape), col="red")
    ## End(Not run)

[Package VGAM version 0.7-9 Index]