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
>
>

```

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