RRrectangular: Random scaling used with balls
In RandomFields: Simulation and Analysis of Random Fields

Description Usage Arguments Details Value See Also Examples

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

1 2	RRrectangular(phi, safety, minsteplen, maxsteps, parts, maxit, innermin, outermax, mcmc_n, normed, approx, onesided)

`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.

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

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

The function φ might have a polynomial pole at the origin and asymptotical decreasing of the form x^β exp(-x^δ).

RRrectangular returns an object of class RMmodel.

RMmodel, RRdistr, RRgauss.

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))