1.
MSV 36: Poisson or not?

2. Hattie and Gerald are given a data set of frequencies to analyse.
They calculate
the mean and variance of the data.
Both are
close to 10.

3. ‘The mean and variance for the Poisson distribution are equal,’
thinks Hattie.
‘Could we have a Poisson here?’
she wonders.

4. (Incidently, both Hattie and Gerald count the Poisson Distribution as their favourite...)

5. ‘The mean and variance for a Poisson distribution
are equal’, says Gerald.
‘But the converse
is not true!
So there are
distributions with ‘mean equals variance’
that look nothing like the Poisson!’

6. Hattie and Gerald decide to construct the simplest least Poisson-like
distribution that they can
so that mean = variance = 10.
Try this!

7. This distribution looks about as un-Poisson-like as we can get.
An Answer
This distribution looks about as un-Poisson-like as we can get.
Clearly here E(X) = 0. We can make E(X) = 10 by later adding 10 to all the values, without altering the variance.

9. Now we can add 10 onto all the values...
So the probability distribution above has mean 10,
and variance 10, but looks nothing like a Poisson distribution.
So if your data has a mean and a variance that are close,
this is a HINT that you could be dealing
with a Poisson distribution, but nothing more!

10. is written by Jonny Griffiths
With thanks to pixabay.com
is written by Jonny Griffiths