urdgt: UNU.RAN discrete random variate generator

Description

UNU.RAN random variate generator for discrete distributions with given probability vector. It applies the Guide-Table Method (urdgt) for discrete inversion or the Alias-Urn Method (urdau).

Usage

urdgt(n, probvector, from = 0, by = 1)
urdau(n, probvector, from = 0, by = 1)

Arguments

size of required sample.

probvector

vector of non-negative numbers (need not sum to 1).

from

number corresponding to the first probability in probvector.

"from + (k-1)*by" is the number corresponding to the $k$-th probability in probvector.

Details

These routines generate a sample of discrete random variates with given probability vector. This vector must be provided by probvector, a vector of non-negative numbers which need not necessarily sum up to 1.

Method DGT uses a guide-table based inversion method.

Method DAU implements the Alias-Urn method.

Both methods run in constant time, i.e., the marginal sampling times do not depend on the length of the given probability vector. Whereas their setup times grow linearly with this length.

References

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

H.C. Chen and Y. Asau (1974): On generating random variates from an empirical distribution. AIIE Trans. 6, pp.163--166.

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

Examples

Run this code

## Create a sample of size 10000 for a 
## binomial distribution with size=115, prob=0.5
x <- urdgt(n=10000, probvector=dbinom(0:115,115,0.5))

## same but with method DAU
x <- urdau(n=10000, probvector=dbinom(0:115,115,0.5))

## Creata a sample of size 10000 standard normal variates rounded to two
## decimal places 
x <- urdgt(n=10000, probvector=dnorm(seq(-5,5,0.01)), from=-5, by=0.01)