RRrectangular {RandomFields}

R Documentation

Random scaling used with balls

Description

Approximates an isotropic decreasing density function by a density function that is isotropic with respect to the l_1 norm.

Usage

RRrectangular(phi, safety, minsteplen, maxsteps, parts, maxit,
             innermin, outermax, mcmc_n, normed, approx, onesided) 

Arguments

phi	a shape function; it is the user's responsibility that it is non-negative. See Details.
safety, minsteplen, maxsteps, parts, maxit, innermin, outermax, mcmc_n	Technical arguments to run an algorithm to simulate from this distribution. See RFoptions for the default values.
normed	logical. If FALSE then the norming constant c in the Details is set to 1. This affects the values of the density function, the probability distribution and the quantile function, but not the simulation of random variables.
approx	logical. Default is TRUE. If TRUE the isotropic distribution with respect to the l_1 norm is returned. If FALSE then the exact isotropic distribution with respect to the l_2 norm is simulated. Neither the density function, nor the probability distribution, nor the quantile function will be available if approx=TRUE.
onesided	logical. Only used for univariate distributions. If TRUE then the density is assumed to be non-negative only on the positive real axis. Otherwise the density is assumed to be symmetric.

Details

This model defines an isotropic density function $f$ with respect to the l_1 norm, i.e. f(x) = c \phi(\|x\|_{l_1}) with some function \phi. Here, c is a norming constant so that the integral of f equals one.

In case that \phi is monotonically decreasing then rejection sampling is used, else MCMC.

The function \phi might have a polynomial pole at the origin and asymptotical decreasing of the form x^\beta exp(-x^\delta).

Value

RRrectangular returns an object of class RMmodel.

Author(s)

Martin Schlather, schlather@math.uni-mannheim.de, https://www.wim.uni-mannheim.de/schlather/

See Also

RMmodel, RRdistr, RRgauss.

Examples

RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
##                   RFoptions(seed=NA) to make them all random again
# simulation of Gaussian variables (in a not very straightforward way):
distr <- RRrectangular(RMgauss(), approx=FALSE)
z <- RFrdistr(distr, n=1000000)
hist(z, 200, freq=!TRUE)
x <- seq(-10, 10, 0.1)
lines(x, dnorm(x, sd=sqrt(0.5)))


#creation of random variables whose density is proportional
# to the spherical model:
distr <- RRrectangular(RMspheric(), approx=FALSE)
z <- RFrdistr(distr, n=1000000)
hist(z, 200, freq=!TRUE)

x <- seq(-10, 10, 0.01)
lines(x, 4/3 * RFcov(RMspheric(), x))

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