VGAM (version 1.1-12)

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.

Arguments

lshape, gshape

Details at CommonVGAMffArguments.

nrfs, zero, parallel

Details at CommonVGAMffArguments.

Author

T. W. Yee

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)