Re: binomial distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg33670] Re: [mg33658] binomial distribution*From*: "Johannes Ludsteck" <johannes.ludsteck at wiwi.uni-regensburg.de>*Date*: Sat, 6 Apr 2002 00:48:44 -0500 (EST)*Organization*: Universitaet Regensburg*Sender*: owner-wri-mathgroup at wolfram.com

Dear Nadia, you seem to be one of the millions of users trying to obtain good answers to *bad* questions! How should someone answer your question if he does not know 1) How large were N and X[[N]] when the error message was given, was it 500 or 10^20? 2) how is p defined? 3) Which program do you use to generate the lists, Nest, FoldList, Do, For? By the way: X[[n]] may increase rapidly (of course, depending on the definition of p). Thus, if for example X[[n]] == 1000, it becomes computationally very demanding to draw 'good' random numbers from a binomial distribution. (If you are interested in the details, have a look at the Package where the random draws are programmed. A simple algorithm is to make thousand (!) draws from a Bernoulli Distribution with parameter p.) However, it is **highly!** inefficient to draw from a binomial distribution if X[[n]] > 100, since (you should have learned this in an introductory statistics course) the binomial distribution converges rapidly to a normal distribution and it is computationally very 'cheap' to draw from a normal distribution. Thus you simply have to transform the binomial distribution to a normal if X > 100 or so. When I replicate your what you *probably* did, I obtain In[1]:= p=Table[Random[Real,{0.1,0.5}],{40}]; In[2]:= FoldList[ #1+Random[BinomialDistribution[#1,#2]]&,1,p] Out[2]= {1,1,1,1,1,1,1,1,1,1,2,3,3,3,4,4,6,8,8,9, 10,11,14,19,26,36,43,55,75,94,122,166,210, 268,396,564,640,831,1187,1757,2068} Though my values in p are between 0.1 and 0.5 and X[[1]] = 1, X[[40]] is larger than 2000. Therefore I advise you to use the normal distribution transformation. Best regards, Johannes On 4 Apr 2002, at 19:40, Nadia Lalam wrote: Hello, I have to define a sequence recursively with the binomial distribution in the following way : X[[n+1]]=X[[n]]+Random[BinomialDistribution[X[[n]],p[[n]]], n ranging from 1 to some N The first terms of the sequence are well constructed with Mathematica but as X[[n]] grows, I had the message Internal counter overflow. Some expression evaluations may not run to their final fixed points. Try redoing your computation on a 64-bit enhanced version of Mathematica. Could you tell me how to solve this problem? Thanks in advance, Nadia