# dau.new: UNU.RAN generator based on the Alias method (DAU) In Runuran: R Interface to the 'UNU.RAN' Random Variate Generators

## Description

UNU.RAN random variate generator for discrete distributions with given probability vector. It applies the Alias-Urn method (‘DAU’).

[Universal] – Patchwork Method.

## Usage

 ```1 2``` ```dau.new(pv, from=1) daud.new(distr) ```

## Arguments

 `pv` vector of non-negative numbers (need not sum to 1). (numeric vector) `from` index of first entry in vector. (integer) `distr` distribution object. (S4 object of class `"unuran.discr"`)

## Details

This function creates a `unuran` object based on ‘DAU’ (Discrete Alias-Urn method). It can be used to draw samples of a discrete random variate with given probability vector using `ur`.

Vector `pv` must be postive but need not be normalized (i.e., it can be any multiple of a probability vector).

The method runs fast in constant time, i.e., marginal sampling times do not depend on the length of the given probability vector. Whereas their setup times grow linearly with this length.

Notice that the range of random variates is `from:(from+length(pv)-1)`.

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

## Value

An object of class `"unuran"`.

## Author(s)

Josef Leydold and Wolfgang H\"ormann [email protected].

## References

W. H\"ormann, J. Leydold, and G. Derflinger (2004): Automatic Nonuniform Random Variate Generation. Springer-Verlag, Berlin Heidelberg. See Section 3.2 (The Alias Method).

A.J. Walker (1977): An efficient method for generating discrete random variables with general distributions. ACM Trans. Model. Comput. Simul. 3, pp.253–256.

`ur`, `unuran.discr`, `unuran.new`, `unuran`.
 ```1 2 3 4 5 6 7 8 9``` ```## Create a sample of size 100 for a ## binomial distribution with size=115, prob=0.5 gen <- dau.new(pv=dbinom(0:115,115,0.5), from=0) x <- ur(gen,100) ## Alternative approach distr <- udbinom(size=100,prob=0.3) gen <- daud.new(distr) x <- ur(gen,100) ```