Runuran (version 0.40)

mixt.new: UNU.RAN generator for finite mixture of distributions

Description

UNU.RAN random variate generator for a finite mixture of continuous or discrete distributions. The components are given as unuran objects.

[Universal] -- Composition Method.

Usage

mixt.new(prob, comp, inversion=FALSE)

Value

An object of class "unuran".

Arguments

prob

weights of mixture (“probabilities”); these must be non-negative numbers but need not sum to 1. (numeric vector)

comp

components of mixture. (list of S4 object of class "unuran")

inversion

whether inversion method should be used. (boolean)

Author

Josef Leydold and Wolfgang H\"ormann .

Details

Given a set of probability density functions \(p_1(x),\dots,p_n(x)\) (called the mixture components) and weights \(w_1,\dots,w_n\) such that \(w_i \ge 0\) and \(\sum w_i = 1\), the sum $$q(x) = \sum_{i=1}^n \, w_i \, p_i(x)$$ is called the mixture density.

Function mixt.new creates an unuran object for a finite mixture of continuous or discrete univariate distributions. It can be used to draw samples of a continuous random variate using ur.

The weights prob must be a vector of non-negative numbers (not all equal to 0) but need not sum to 1.

comp is a list of "unuran" generator objects. Each of which must sample from a continuous or discrete univariate distribution.

If inversion is TRUE, then the inversion method is used for sampling from the mixture distribution. However, the following conditions must be satisfied:

• Each component (unuran object) must use implement an inversion method (i.e., the quantile funtion uq must work).

• The domains of the components must not overlapping.

• The components must be order with respect to their domains.

If one of these conditions is violated, then initialization of the mixture object fails.

The setup time is fast, whereas its marginal generation times strongly depend on the average generation times of its components.

References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg. See Section 2.3 (Composition).

See Also

ur, uq, unuran.new, unuran.

Examples

## Create a mixture of an Exponential and a Half-normal distribution
unr1 <- unuran.new(udnorm(lb=-Inf, ub=0))
unr2 <- unuran.new(udexp())
mix <- mixt.new( c(1,1), c(unr1, unr2) )
x <- ur(mix,100)

## Now use inversion method:
## It is important that
##  1. we use a inversion for each component
##  2. the domains to not overlap
##  3. the components are ordered with respect to their domains
unr1 <- pinvd.new(udnorm(lb=-Inf, ub=0))
unr2 <- pinvd.new(udexp())
mix <- mixt.new( c(1,1), c(unr1, unr2), inversion=TRUE )
x <- ur(mix,100)

## We also can compute the inverse distribution function
##x <- uq(mix,0.90)

## Create a mixture of Exponential and Geometric distrbutions
unr1 <- unuran.new(udexp())
unr2 <- unuran.new(udgeom(0.7))
mix <- mixt.new( c(0.6,0.4), c(unr1, unr2) )
x <- ur(mix,100)