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VGAM (version 1.1-11)

Hurea: The Husler-Reiss Angular Surface Distribution

Description

Density for the Husler-Reiss angular surface distribution.

Usage

dhurea(x, shape, log = FALSE)

Value

dhurea gives the density.

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.

Author

T. W. Yee

Warning

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

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.

See Also

hurea.

Examples

Run this code
integrate(dhurea, 0, 1, shape = 0.20)  # Incorrect
integrate(dhurea, 0, 1, shape = 0.35)  # struggling but okay
if (FALSE) 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")

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