Hurea {VGAM}

The Husler-Reiss Angular Surface Distribution

Description

Density for the Husler-Reiss angular surface distribution.

Usage

dhurea(x, shape, log = FALSE)

Arguments

x

Same as Uniform.

shape

the positive (shape) parameter. It is often called lambda and it might not be a shape parameter at all.

log

Logical. If log = TRUE then the logarithm of the density is returned.

Details

See hurea, the VGAM family function for estimating the (shape) parameter s by maximum likelihood estimation, for the formula of the probability density function.

Value

dhurea gives the density.

Warning

The cases x == 0, x == 1, shape == 0 and shape == Inf may not be handled correctly.

Note

Difficulties are encountered as the shape parameter approaches 0 with respect to integrate because the density converges to a degenerate distribution with probability mass at 0 and 1. That is, when s is around 0.5 the density is “u” shaped and the area around the endpoints becomes concentrated at the two points. See the examples below. Approximately, the density is “u” shaped for s < 1 and unimodal for s > 2.

Author(s)

T. W. Yee

See Also

hurea.

Examples

integrate(dhurea, 0, 1, shape = 0.20)  # Incorrect
integrate(dhurea, 0, 1, shape = 0.35)  # struggling but okay
## Not run: x <- seq(0, 1, length = 501)
par(mfrow = c(2, 2))
plot(x, dhurea(x, 0.7), col = "blue", type = "l")
plot(x, dhurea(x, 1.1), col = "blue", type = "l")
plot(x, dhurea(x, 1.4), col = "blue", type = "l")
plot(x, dhurea(x, 3.0), col = "blue", type = "l")

## End(Not run)