VGAM (version 1.1-14)

hurea: Husler-Reiss Angular Surface Distribution Family Function

Description

Estimating the parameter of the Husler-Reiss angular surface distribution by maximum likelihood estimation.

Usage

hurea(lshape = "loglink", zero = NULL, nrfs = 1,
      gshape = exp(3 * ppoints(5) - 1), parallel = FALSE)

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm, and vgam.

Details

The Husler-Reiss angular surface distribution has a probability density function that can be written $$f(y;s) = (s / (4 * sqrt(2*pi) * y(1-y)^2)) exp(-(2 + s^2 * logit y)^2 / [8 s^2])$$ for \(0<y<1\) and positive shape parameter \(s\). The mean of \(Y\) is currently unknown to me, as well as its quantiles. Hence \(s\) is currently returned as the fitted values. Fisher-scoring is implemented.

References

Mhalla, L. and de Carvalho, M. and Chavez-Demoulin, V. (2019). Regression-type models for extremal dependence. Scandinavian Journal of Statistics, 46, 1141--1167.

See Also

hurea.

Examples

nn <- 100; set.seed(1)
hdata <- data.frame(x2 = runif(nn))
hdata <-
  transform(hdata,  # Cannot generate proper random variates!
    y1 = rbeta(nn, shape1 = 0.5, shape2 = 0.5),  # "U" shaped
    y2 = rnorm(nn, 0.65, sd = exp(-3 - 4 * x2)))
# Multiple responses:
hfit <- vglm(cbind(y1, y2) ~ x2, hurea, hdata, trace = TRUE)
coef(hfit, matrix = TRUE)
summary(hfit)