Poisson distribution

[Chris Harris]

I have a quick question I'm hoping somebody can help me with:

I have a distribution of values which are rare event count data
(annual complaints filed against police officers). I want to compare
this distribution to the Poisson distribution to determine if it
differs from chance (and if so, by how much). While I know this is
certainly possible, I'm uncertain as to the mechanics of doing so in
SPSS. Ideally I'm envisioning a table where I have the frequency
distribution of the values, along with the expected values based on
the Poisson distribution.

Anyone know how to do this?

Thanks!

[Bruce Weaver]

Perhaps the examples here will be useful:

http://www.zoology.ubc.ca/~whitlock/bio300/lecturenotes/gof/gof.html

The "Prussian Cavalry getting kicked in the head" example seems similar
to your problem.

--
Bruce Weaver
bwe...@lakeheadu.ca
http://sites.google.com/a/lakeheadu.ca/bweaver/Home
"When all else fails, RTFM."

[Chris Harris]

On Jan 18, 9:11 am, Bruce Weaver <bwea...@lakeheadu.ca> wrote:
> On 18/01/2012 8:29 AM, Chris Harris wrote:
>
> > I have a quick question I'm hoping somebody can help me with:
>
> > I have a distribution of values which are rare event count data
> > (annual complaints filed against police officers).  I want to compare
> > this distribution to the Poisson distribution to determine if it
> > differs from chance (and if so, by how much).  While I know this is
> > certainly possible, I'm uncertain as to the mechanics of doing so in
> > SPSS.  Ideally I'm envisioning a table where I have the frequency
> > distribution of the values, along with the expected values based on
> > the Poisson distribution.
>
> > Anyone know how to do this?
>
> > Thanks!
>
> Perhaps the examples here will be useful:
>
>    http://www.zoology.ubc.ca/~whitlock/bio300/lecturenotes/gof/gof.html
>
> The "Prussian Cavalry getting kicked in the head" example seems similar
> to your problem.
>
> --
> Bruce Weaver

> bwea...@lakeheadu.cahttp://sites.google.com/a/lakeheadu.ca/bweaver/Home

> "When all else fails, RTFM."

Yes, it certainly does. Thank you.

Can I ask: how were the expected frequencies of the number of deaths
per year calculated from the rate of .61, given the Poisson
distribution? It's not clear from the example.

[Andy W]

It is taken from the mean of the observed distribution.

Raynald has a script on his site that has the same goals as you (both
a table and a test statistic is produced)
http://spsstools.net/Syntax/Distributions/GoodnessOfFitTestForPoissonDistr.txt

Although I expect a visual inspection of deviations would suffice in
many circumstances (foregoing the need for a statistical test).

This question on the stats.se forum
http://stats.stackexchange.com/q/1174/1036
has some references for another inferential test as well, seeing if
the variance of the distribution equals the mean.

Andy W

[Art Kendall]

* this demonstration shows some concepts about Poisson distributions.
data list list /hits (f1).
begin data.
0
1
2
3
4
5
end data.
compute meanhits = .61.
compute probexact = pdf.poisson(hits,meanhits).
do if hits eq 0.
compute problower = 0.
compute cumprob1 = probexact.
compute cumprob2 = probexact.
else.
compute problower = lag(cumprob1).
compute cumprob1 = probexact+lag(cumprob1).
compute cumprob2 = cdf.poisson(hits,meanhits).
end if.
compute probhigher = 1-cumprob1.
formats meanhits probexact cumprob1 cumprob2 problower probhigher (f6.5).
list.

*CDF.POISSON. CDF.POISSON(quant, mean). Numeric. Returns the cumulative
probability
that a value from the Poisson distribution, with the specified mean or
rate parameter,
will be less than or equal to quant.
*PDF.POISSON. PDF.POISSON(quant, mean). Numeric. Returns the probability
that a value from the Poisson distribution, with the specified mean or
rate parameter,
will be equal to quant.
* Help > Algorithms > Distribution and Special Functions > Discrete
Distributions (Distribution and Special Functions algorithms)


Art Kendall
Social Research Consultants