frechet.RdMaximum likelihood estimation of the 2-parameter Frechet distribution.
frechet(location = 0, lscale = "loglink",
lshape = logofflink(offset = -2),
iscale = NULL, ishape = NULL, nsimEIM = 250, zero = NULL)Numeric. Location parameter. It is called \(a\) below.
Link functions for the parameters;
see Links for more choices.
See CommonVGAMffArguments for information.
The (3-parameter) Frechet distribution has a density function that can be written $$f(y) = \frac{sb}{ (y-a)^2} [b/(y-a)]^{s-1} \, \exp[-(b/(y-a))^s] $$ 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 \(b^2 [ \Gamma(1-2/s) - \Gamma^2(1-1/s)]\) 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.
An object of class "vglmff"
(see vglmff-class).
The object is used by modelling functions such
as vglm
and vgam.
Castillo, E., Hadi, A. S., Balakrishnan, N. and Sarabia, J. S. (2005). Extreme Value and Related Models with Applications in Engineering and Science, Hoboken, NJ, USA: Wiley-Interscience.
Family function frechet may fail for low values of
the shape parameter, e.g., near 2 or lower.
if (FALSE) { # \dontrun{
set.seed(123)
fdata <- data.frame(y1 = rfrechet(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)
} # }