R: Random scaling used with balls

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 responsability 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 the density function, the probability distribution and the quantile function, but not the simulation of random variables.
`approx` | logical. Default `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, not the quantile function will be availabe if `approx=TRUE`.
`onesided` | logical. Only for 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 models 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, s is norming constant so that the integral of f equals one.

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

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

### Value

`RRrectangular` returns an object of class `RMmodel`

### Author(s)

Martin Schlather, schlather@math.uni-mannheim.de

### 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 straight forward 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))

[Package RandomFields version 3.1.50 Index]