hkevp (version 1.1.6)

hkevp.rand: Simulation of the HKEVP

Description

Simulation procedure of the HKEVP with given sites and knots positions and marginal and spatial dependence parameters.

Usage

hkevp.rand(nrep, sites, knots, loc, scale, shape, alpha, tau)

Value

A numerical matrix of real values. Each column corresponds to a position and each row to a realisation of the process.

Arguments

nrep

A positive integer. Number of realisations of the block mashapema process.

sites

The coordinates of the sites where the data are observed. Each row corresponds 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.

loc

A numerical value or a vector of real values for the GEV location parameter. If a vector, its length must coincide with the number of sites. The value by default is 1.

scale

A numerical value or a vector of real values for the GEV scale parameter. If a vector, its length must coincide with the number of sites. The value by default is 1.

shape

A numerical value or a vector of real values for the GEV shape parameter. If a vector, its length must coincide with the number of sites. The value by default is 1.

alpha

The dependence parameter \(\alpha\) of the HKEVP: a single value in (0,1].

tau

The bandwidth parameter \(\tau\) of the kernel functions in the HKEVP: a positive value.

Author

Quentin Sebille

Details

Simulating one realisation of the block mashapema process \(Y(\cdot)\) from the HKEVP involves three steps:

1. The nugget process \(U(\cdot)\) is generated independently at each position, by simulating a random variable with \(GEV(1,\alpha,\alpha)\) distribution.

2. The residual dependence process \(\theta(\cdot)\) is computed by using the kernel functions centered at the set of knots, the bandwidth parameter \(\tau\) and the simulations of the positive stable \(PS(\alpha)\) random effect \(A\).

3. The process \(Z = U\theta\) is computed and its margins are transformed to the general GEV distribution with \(\mu(s),\sigma(s)\) and \(\xi(s)\) parameters.

Examples

# Simulation of HKEVP:
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)