Frechet Distribution Family Function
Maximum 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)location |
Numeric. Location parameter. It is called a below. |
lscale, lshape |
Link functions for the parameters;
see |
iscale, ishape, zero, nsimEIM |
See |
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.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm
and vgam.
Family function frechet may fail for low values of
the shape parameter, e.g., near 2 or lower.
T. W. Yee
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.
## 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)
Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.