Runuran (version 0.40)

srou.new: UNU.RAN generator based on Simple Ratio-Of-Uniforms Method (SROU)

Description

UNU.RAN random variate generator for continuous distributions with given probability density function (PDF). It is based on the Simple Ratio-Of-Uniforms Method (‘SROU’).

[Universal] -- Rejection Method.

Usage

srou.new(pdf, lb, ub, mode, area, islog=FALSE, r=1, ...)
sroud.new(distr, r=1)

Value

An object of class "unuran".

Arguments

pdf

probability density function. (R function)

lb

lower bound of domain; use -Inf if unbounded from left. (numeric)

ub

upper bound of domain; use Inf if unbounded from right. (numeric)

mode

location of the mode. (numeric)

area

area below pdf. (numeric)

islog

whether pdf is given as log-density (the dpdf must then be the derivative of the log-density). (boolean)

...

(optional) arguments for pdf.

distr

distribution object. (S4 object of class "unuran.cont")

r

adjust algorithm to heavy-tailed distribution. (numeric)

Author

Josef Leydold and Wolfgang H\"ormann .

Details

This function creates a unuran object based on ‘SROU’ (Simple Ratio-Of-Uniforms Method). It can be used to draw samples of a continuous random variate with given probability density function using ur.

The density pdf must be positive but need not be normalized (i.e., it can be any multiple of a density function). It must be \(T_c\)-concave for \(c = -r/(r+1)\); this includes all log-concave distributions.

The (exact) location of the mode and the area below the pdf are essential.

Alternatively, one can use function sroud.new where the object distr of class "unuran.cont" must contain all required information about the distribution.

The acceptance probability decreases with increasing parameter r. Thus it should be as small as possible. On the other hand it must be sufficiently large for heavy tailed distributions. If possible, use the default r=1.

Compared to tdr.new it has much slower marginal generation times but has a faster setup and is numerically more robust. Moreover, It also works for unimodal distributions with tails that are heavier than those of the Cauchy distribution.

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg. Sections 6.3 and 6.4.

See Also

ur, unuran.cont, unuran.new, unuran.

Examples

## Create a sample of size 100 for a Gaussian distribution.
pdf <- function (x) { exp(-0.5*x^2) }
gen <- srou.new(pdf=pdf, lb=-Inf, ub=Inf, mode=0, area=2.506628275)
x <- ur(gen,100)

## Create a sample of size 100 for a Gaussian distribution.
## Use 'dnorm'.
gen <- srou.new(pdf=dnorm, lb=-Inf, ub=Inf, mode=0, area=1)
x <- ur(gen,100)

## Alternative approach
distr <- udnorm()
gen <- sroud.new(distr)
x <- ur(gen,100)