Re: Fit to Poisson Distribution

From: Lasse Rasmussen (lasse.ras_at_gmail.com)
Date: 06/28/04 

Date: 27 Jun 2004 23:42:48 -0700

Oops, I put the variable 'a' the wrong place. The model equation should be:

P(x+a)=m^x Exp(-m)/x!

or

P(x)=m^(x-a) Exp(-m)/(x-a)!

if you prefer.

So it is essentially a Poisson distribution shifted to the right by a.

Lasse

> I have a couple of basic questions related to fitting data to a
> Poisson distribution.
>
> I have about 100 data points and when I plot the data it looks like a
> Poisson distribution plus a constant number. I think the underlying
> process is indeed a Poisson process with a constant so that's good,
> but I want to achieve a good estimation of the two variables in my
> model (the constant and the poisson process mean/variance). My model
> distribution therefore looks like this
>
> P(x)=a+m^x Exp(-m)/x! ,
>
> where a is the constant and m is the mean/variance of the Poisson
> distribution.
>
> If I simply calculate the average value of the data points and the
> variance, I can deduce a and m, since m must be equal to the variance
> and a+m must be equal to the average value of the data points. If I
> then calculate the chi-square value using an appropriate number of
> bins, I am well within a 5% confidence level (I hope this approach is
> statistically sound...). Ie. my chi-square value is sufficiently low.
>
> However, is this the best to way fit my data to the proposed model?
> Should I instead use a least squares method to obtain a better fit? I
> suspect my assumption that a+m equals the average of the data points
> constrains my fit somewhat.
>
> Also, I am not sure I use the correct number of degrees of freedom.
> With 8 data bins and two contraints (a+m=average value of data points
> and m=variance) I have 6 degrees of freedom. Is this correct?
>
> Thanks,
>
> Lasse

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