R: The Frechet Distribution

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,
             lower.tail = TRUE, log.p = FALSE)
    qfrechet(p, location = 0, scale = 1, shape,
             lower.tail = TRUE, log.p = FALSE)
    rfrechet(n, location = 0, scale = 1, shape)

### Arguments

`x, q` | vector of quantiles.
`p` | vector of probabilities.
`n` | number of observations. Passed into `runif`.
`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.
`lower.tail, log.p` | Same meaning as in `punif` or `qunif`.

### Details

See `frechet`, the VGAM family function for estimating the 2 parameters (without location parameter) 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 and Kai Huang

### References

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

### See Also

`frechet`.

### Examples

    ## Not run:  shape <- 5
    x <- seq(-0.1, 3.5, length = 401)
    plot(x, dfrechet(x, shape = shape), type = "l", ylab = "", las = 1,
         main = "Frechet density divided into 10 equal areas; orange = 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 = "orange")

    ## End(Not run)

[Package VGAM version 1.1-3 Index]