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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
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