frechet {VGAM} | R Documentation

## Frechet Distribution Family Function

### Description

Maximum likelihood estimation of the 2-parameter Frechet distribution.

### Usage

    frechet(location = 0, lscale = "loglink", lshape = logofflink(offset = -2),
            iscale = NULL, ishape = NULL, nsimEIM = 250, zero = NULL)

### Arguments

`location` | Numeric. Location parameter. It is called a below.
`lscale, lshape` | Link functions for the parameters; see `Links` for more choices.
`iscale, ishape, zero, nsimEIM` | See `CommonVGAMffArguments` for information.

### Details

The (3-parameter) Frechet distribution has a density function that can be written

f(y) = ((s*b) / (y-a)^2) * exp[-(b/(y-a))^s] * [b/(y-a)]^(s-1)

for y > a and scale parameter b > 0. The positive shape parameter is s. The cumulative distribution function is

F(y) = exp[-(b/(y-a))^s].

The mean of Y is a + b*gamma(1-1/s) for s > 1 (these are returned as the fitted values). The variance of Y is b^2 * [gamma(1 - 2/s) - gamma(1 - 1/s)^2] for s > 2.

Family `frechet` has a known, and log(b) and log(s - 2) are the default linear/additive predictors. The working weights are estimated by simulated Fisher scoring.

### Value

An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm` and `vgam`.

### Warning

Family function `frechet` may fail for low values of the shape parameter, e.g., near 2 or lower.

### 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, NJ, USA: Wiley-Interscience.

### See Also

`rfrechet`, `gev`.

### Examples

    ## Not run:
    set.seed(123)
    fdata <- data.frame(y1 = rfrechet(nn <- 1000, shape = 2 + exp(1)))
    with(fdata, hist(y1))
    fit2 <- vglm(y1 ~ 1, frechet, data = fdata, trace = TRUE)
    coef(fit2, matrix = TRUE)
    Coef(fit2)
    head(fitted(fit2))
    with(fdata, mean(y1))
    head(weights(fit2, type = "working"))
    vcov(fit2)

    ## End(Not run)

[Package VGAM version 1.1-1 Index]