RE: Second Opinion

*To*: mathgroup at smc.vnet.net*Subject*: [mg26378] RE: [mg26373] Second Opinion*From*: "Todd Stevenson" <todds at wolfram.com>*Date*: Sat, 16 Dec 2000 02:40:10 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

The Standard Add-on Package contains the Poisson Distribution of the form <<Statistics`DiscreteDistributions` P(X=x) = (Exp[-n]*n^x)/Factorial[x] which is different than the one you are using. Yours seems to be 1 minus the CDF of the Poisson: 1 - CDF[PoissonDistribution[n],N-1] I don't know whether that is the problem or not, but you should be able to combine the functions in this standard add-on with Plot[] to get a feel for what's going on. Todd Stevenson Wolfram Research > -----Original Message----- > From: owner-wri-mathgroup [mailto:owner-wri-mathgroup]On Behalf Of John To: mathgroup at smc.vnet.net > Lai > Sent: Wednesday, December 13, 2000 1:42 AM > To: mathgroup at smc.vnet.net > Subject: [mg26378] [mg26373] Second Opinion > > > 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 > >