simulating random variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg32831] simulating random variables*From*: "Aaron E. Hirsh" <aehirsh at stanford.edu>*Date*: Thu, 14 Feb 2002 01:44:02 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Dear All, I need to simulate a large number of binomial random variables. Unfortunately, when the parameter n (number of trials) is large, the simulation of binomial random variables is relatively time consuming. For example, if I would like to simulate a binomial random variable with parameters n = 10000 and p =0.01: In[134]:= Timing[Random[BinomialDistribution[100000,0.01]]] Out[134]= {0.283333 Second,1007} One possibility for saving time would be to use an approximation. For small p, an appropriate approximation is the Poisson. While this is definitely better: In[135]:= Timing[Random[PoissonDistribution[(.01)(100000)]]] Out[135]= {0.0333333 Second,1002} , it is still much slower than using a normal: In[136]:= \!\(Timing[ Random[NormalDistribution[(.01)(100000),((.01)(100000)(.99))^0.5]]]\) Out[136]= {0. Second,1025.3} Does anyone know how I could speed up my simulation of binomial or poisson-distributed random variables? I would also be interested in ways of speeding up the simulation of the Normal, though it seems extraordinarily efficient already. Thank you very much, Aaron Hirsh -- Aaron E. Hirsh Center for Computational Genetics and Biological Modeling Stanford University tel. (650) 723-4952 fax. (650) 725-0180

**Follow-Ups**:**Re: simulating random variables***From:*Tomas Garza <tgarza01@prodigy.net.mx>