frechet {VGAM}R Documentation

Frechet Distribution Family Function

Description

Maximum likelihood estimation of the 2-parameter Frechet distribution.

Usage

frechet2(location = 0, lscale = "loge", lshape = "logoff",
         escale = list(), eshape = list(offset = -2), iscale = NULL,
         ishape = NULL, nsimEIM = 250, zero = NULL)




Arguments

location

Numeric. Location parameter. It is called a below.

lscale, lshape, escale, eshape

Link functions and extra arguments 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 frechet2 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 frechet2 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, N.J.: Wiley-Interscience.

See Also

rfrechet, gev.

Examples

set.seed(123)
fdata = data.frame(y1 = rfrechet(nn <- 1000, shape = 2 + exp(1)))
## Not run:  with(fdata, hist(y1)) 
fit2 = vglm(y1 ~ 1, frechet2, fdata, trace = TRUE)
coef(fit2, matrix = TRUE)
Coef(fit2)
head(fitted(fit2))
with(fdata, mean(y1))
head(weights(fit2, type = "working"))
vcov(fit2)

[Package VGAM version 0.8-4 Index]