Second Opinion

*To*: mathgroup at smc.vnet.net*Subject*: [mg26373] Second Opinion*From*: "John Lai" <john.lai at worldnet.att.net>*Date*: Wed, 13 Dec 2000 02:41:30 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Hello all, I tried to calculate Poisson Distribution in a backdoor way and used mathematica to model it. I could not get what I wanted. I don't think it is mathematica problem and more than likely my method is flawed. So I toss this out to see if some of you may spot my error. Poisson Distribution,P(n) =1-Summation [exp(-n)*(n^x)]/Factorial(x) where x goes from 0 to N-1 For given n and N, P(n) can be determined easily. However, I want to determine N if P(n) and n are specified and I do not want to get access to Poisson lookup table. My idea is to calculate P(n) with a series of n and N (essentially generating the tables). Plot a surface curve whose variables are n, P(n) and N. The idea was once this surface is obtained, with x-axis as n, y-axis as P(n) and z-axis as N, then for a given n and P(n) I can obtain N. I wrote a C program to generate P(n) and use mathematica to plot this surface. I have 14 sets of n and in each set of n, I have 139 variables (i.e. N runs from 1 to 140 ), so there are 139 corresponding values of P(n) for each n. When I tried to use the function Fit to estimate this surface, it took about ½ hr for my 500MHz desktop to calculate! And the resultant expression is huge! Then, I cut down the dimension of my data set. For each n, I generated 10 values of N and repeated the process again. However, no matter what combination of polynomial I used (x,x^-1,Exp(-x),Exp(-x^2),Exp(-x-y).), the resulting equation of the surface is meaningless. It doesn't look right (at least I expected it to resemble some sort of Poisson or even Gaussian shape) and substituting P(n) and n back, I got garbage. I have enclosed a .nb file for reference. [Contact the author to obtain this file - moderator] So after all this, does it mean that my scheme of calculating Poisson Distribution is fundamentally wrong? Any suggestions are appreciated and thanks in advance. John Lai

**Follow-Ups**:**Re: Second Opinion***From:*Daniel Lichtblau <danl@wolfram.com>