# One sided testing of two Poisson distributions?

I want to test if one Poisson distributed result a is large than another one b.
I don't know much about statistics, but I understood the Wiki article about testing normal distribution however they need the number of samples there.

Basically I measure two Poisson distributed variables, I get two values and want to know the probability that one is larger than the other.

Can someone give my a quick reference (online or good book), where I can find my problem as close as possible?

Last edited:

Related Set Theory, Logic, Probability, Statistics News on Phys.org
EnumaElish
Homework Helper
You can compute the difference between the two Poisson means and see whether the difference is significantly different from zero under the Skellam distribution.

Or (with a large enough sample) you can assume that the normal distribution will be a reasonable approximation.

Last edited:
You can compute the difference between the two Poisson means and see whether the difference is significantly different from zero under the Skellam distribution.

Or (with a large enough sample) you can assume that the normal distribution will be a reasonable approximation.
I think I just about know what to do with the Skellam. But it has a funny Bessel function.
I have both means approx. 500.
What would be the method with the normal distribution?

EnumaElish
Homework Helper
If you know the true variances, the z test.

If you are using computed variances, then technically you should use t test with equal or unequal variances, as the case may be. As the sample size increases, the z-test becomes a good approximation to the t-test (e.g. for n > 40).

If you know the true variances, the z test.

If you are using computed variances, then technically you should use t test with equal or unequal variances, as the case may be. As the sample size increases, the z-test becomes a good approximation to the t-test (e.g. for n > 40).
I tried to look through these tests, but I'm not sure what to take. I only know that I measured a single value
x and single value y. Both are supposed to be Poisson (so I expect x+- sqrt(x) and y+-sqrt(y)).

In this case I'm not sure how interpret "computed variance" or "sample size".
I know about mathematics, but not of the formalities of statistics :(

I found the following (attachment) in
"An improved approximate two-sample poisson test" (M.D.Huffman)

Just to make sure I got it right and plug in the right values:
I use $\alpha=0.05, p=0.90$ as sensible values?
I look up z in a table? (i.e. $z_{0.95}=1.65, z_{0.90}=1.28$)
I estimate $\varrho$ from initial measurements.
Should I use equal counting time $d=1$ for best results?
By equation (4) I will find how long I have to measure...

EnumaElish