difference of two independent Poisson random variables

LIPI

New Member
Why the difference of two independent Poisson random variables doesn't have Poisson distribution? Demonstrate it.

Dason

Simplest way to realize this is that the difference can easily be negative but a poisson random variable can't be negative.

LIPI

New Member
I only know how to do the sum of two independent Poisson random variable using moment generating function (by using theorem)but don't know how to do the difference. Can you please explain in some detail how to do the difference.

Dason

Are you asking how to show that the difference *isn't* poisson distributed or how to derive the distribution of the difference?

LIPI

New Member
I have to prove that the difference of two independent Poisson random variables isn't Poisson distribution. I know that the difference of two independent Poisson random variables has a Skellam distribution but for homework I have to prove that the difference is not Poisson Distribution.

This is my homework question.
Determine if the difference of two independent Poisson random variables has a Poisson distribution. If it does, prove it. If it doesn’t, demonstrate why.