# Poission distribution

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• #34586

littleann
Participant

I have a set of data. they are most likely to obey Poission distribution. now i am told to  prove they actually are distributed Poission. what should i do?

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#95508

Tim Folkerts
Member

It is often difficult to “prove” things when random variation is present, but there are a couple things you could do to show that the numbers are consistent with a Poisson distribution.
First, for Poisson distribution, the mean and the variance should be approximately equal, so check these two numbers for your distribution.
Once you know the mean, you could calculate the expected Poisson distribution and compare it graphically to your data.
I also found a web page at http://csssrvr.entnem.ufl.edu/~walker/6203/L1hpoiss.pdf which shows how to test how well data agrees with a Poisson distribution.

Tim

that something For a Poisson distribution, the

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#95513

Isabel
Participant

The characteristic of the Poisson Distribution is that the
mean and the variance have the same value.So you can calculate the mean of your data set, compute
the variance and if they are the same then it means that
your data set has a Poisson distribution.I hope it helps.Isabel

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#95527

Tim Folkerts
Member

I should add one important fact.  It is true that if you have a Poisson distribution, then the mean and variance will be (at least approximately) equal.
HOWEVER, it is not true that if the mean and variance are equal, then it must be a Poisson distribution.  If you have small defect rates, then the binimial distribution will also have the mean and variance approximately equal.  It is also quite possible for a normal distribution to have mean and variance equal.
To really know, you must look at the shape as well.

Tim

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#95529

Andy Sleeper
Participant

I agree with the other replies, but I would like to add one thing.  In general, you can’t prove that a set of data comes from a population with a particular distribution.
There are several goodness-of-fit tests around, including Kolmogorov-Smirnov, Anderson-Darling, and others.  These procedures might show that your data does not come from a certain distribution.  Usually, people assume that if the test fails to reject a certain distribution, then that model is probably valid.  But that’s the same as concluding that because OJ was found “not guilty”, he must be “innocent.”  Maybe, and maybe not.
If I had your data, I would ask about where the data comes from.  Does the data represent counts of “events” in a certain amount of “time” or “space”?  Are the “events” independent of each other?  If so, Poisson is generally recognized as a good model for systems like this.

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