hkevp.expmeasure {hkevp} | R Documentation |
Exponent measure of the HKEVP
Description
Exponent measure of the HKEVP of Reich and Shaby (2012), with given model parameters or output from
hkevp.fit
or latent.fit
.
Usage
hkevp.expmeasure(z, sites, knots, alpha, tau, fit)
Arguments
z |
The vector |
sites |
The coordinates of the sites where the data are observed. Each row correspond to a site position. |
knots |
The coordinates of the knots in the HKEVP. By default, the positions of the knots coincide with the positions of the sites. |
alpha |
The dependence parameter |
tau |
The bandwidth parameter |
fit |
Output from the |
Details
The exponent measure describes the spatial dependence structure of a max-stable process, independently from the values of the marginal parameters. If is a simple max-stable process, i.e. with unit GEV(1,1,1) margins, recorded at the set of sites
, its joint cumulative probability density function is given by:
where is the so-called exponent measure.
For the HKEVP, the exponent measure is explicit for any number
of sites:
If argument fit
is provided, the predictive distribution of
is computed. If not, the function uses arguments sites
, knots
, alpha
, and tau
.
Value
Either a vector if argument fit
is provided, or a single value.
Author(s)
Quentin Sebille
References
Reich, B. J., & Shaby, B. A. (2012). A hierarchical max-stable spatial model for extreme precipitation. The annals of applied statistics, 6(4), 1430. <DOI:10.1214/12-AOAS591>
Examples
sites <- as.matrix(expand.grid(1:3,1:3))
loc <- sites[,1]*10
scale <- 3
shape <- 0
alpha <- .4
tau <- 1
ysim <- hkevp.rand(10, sites, sites, loc, scale, shape, alpha, tau)
# HKEVP fit:
fit <- hkevp.fit(ysim, sites, niter = 1000)
predict.em <- hkevp.expmeasure(1, fit = fit)
true.em <- hkevp.expmeasure(1, sites, sites, alpha, tau)
# plot(predict.em, ylim = range(predict.em, true.em), type = "l")
# abline(h = true.em, col = 2, lwd = 2)