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Last data update: 2014.03.03

R: Random scaling used with balls

RRrectangular

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

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))

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(RandomFields)
Loading required package: sp
Loading required package: RandomFieldsUtils
This is RandomFieldsUtils Version: 0.2.1
This is RandomFields Version: 3.1.16

Attaching package: 'RandomFields'

The following object is masked from 'package:RandomFieldsUtils':

    RFoptions

The following objects are masked from 'package:base':

    abs, acosh, asin, asinh, atan, atan2, atanh, cos, cosh, exp, expm1,
    floor, gamma, lgamma, log, log1p, log2, logb, max, min, round, sin,
    sinh, sqrt, tan, tanh, trunc

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/RandomFields/RRrectangular.Rd_%03d_medium.png", width=480, height=480)
> ### Name: RRrectangular
> ### Title: Random scaling used with balls
> ### Aliases: RRrectangular
> ### Keywords: spatial models
> 
> ### ** Examples
> 
> RFoptions(seed=0) ## *ANY* simulation will have the random seed 0; set
> ##                   RFoptions(seed=NA) to make them all random again
> ## Don't show: 
> StartExample()
> ## End(Don't show)
> # simulation of Gaussian variables (in a not very straight forward way):
> distr <- RRrectangular(RMgauss(), approx=FALSE)
> z <- RFrdistr(distr, n=1000000)
number of simulations reduced
> 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)
number of simulations reduced
> hist(z, 200, freq=!TRUE)
> ## Don't show: 
> StartExample(reduced=FALSE)
> ## End(Don't show)
> x <- seq(-10, 10, 0.01)
> lines(x, 4/3 * RFcov(RMspheric(), x))
> ## Don't show: 
> FinalizeExample()
> ## End(Don't show)
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>