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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>