hureaUC.RdDensity for the Husler-Reiss angular surface distribution.
dhurea(x, shape, log = FALSE)Same as Uniform.
the positive (shape) parameter. It is often called \(lambda\) and it might not be a shape parameter at all.
Logical.
If log = TRUE then the logarithm of the
density is returned.
dhurea gives the density.
See hurea, the VGAM
family function for
estimating the (shape) parameter \(s\) by
maximum likelihood
estimation, for the formula of the
probability density function.
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 \(s > 2\).
The cases x == 0, x == 1,
shape == 0 and
shape == Inf
may not be handled correctly.
integrate(dhurea, 0, 1, shape = 0.20) # Incorrect
#> 1.426387e-05 with absolute error < 2.4e-05
integrate(dhurea, 0, 1, shape = 0.35) # struggling but okay
#> 1.000074 with absolute error < 5.3e-05
if (FALSE) x <- seq(0, 1, length = 501)
par(mfrow = c(2, 2))
plot(x, dhurea(x, 0.7), col = "blue", type = "l")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
plot(x, dhurea(x, 1.1), col = "blue", type = "l")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
plot(x, dhurea(x, 1.4), col = "blue", type = "l")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
plot(x, dhurea(x, 3.0), col = "blue", type = "l")
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'x' in selecting a method for function 'plot': object 'x' not found
# \dontrun{}