hurea {VGAM}

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)

Arguments

lshape, gshape

Details at CommonVGAMffArguments.

nrfs, zero, parallel

Details at CommonVGAMffArguments.

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.

Value

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

Note

This VGAM family function handles multiple responses. It may struggle and/or fail when s is close to 0. Some comments about “u”-shaped versus unimodal densities accommodated by this distribution are at dhurea.

Author(s)

T. W. Yee

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)