0

I've observed two Poisson processes and my goal is to determine whether they came from the same process or not. Is there a test to determine this?

  • Not the same mean - but come from the same process. –  Mar 09 '16 at 18:33
  • 2
    A Poisson process is characterized by its rate parameter, which is essentially a mean, so determining whether or not two processes are the same is equivalent to a test about means. – dsaxton Mar 09 '16 at 18:45
  • Rate does not equivalate to mean –  Mar 09 '16 at 18:45
  • 3
    What is the mean of a Poisson process with rate $\lambda$ at time $t$? (And note the "essentially" in my comment.) – dsaxton Mar 09 '16 at 18:47
  • Let's say the variances were different –  Mar 09 '16 at 23:15
  • The Poisson variance is equal to its mean, as you can easily see from reading the Wikipedia page on the Poisson distribution. That comment suggests a lack of basic research (like reading about basic properties of the Poisson). If you know the variances differ and you know you have Poisson distributions, there's nothing to test --- the means automatically differ. – Glen_b Mar 09 '16 at 23:33
  • let's say that i read wikipedia next time –  Mar 09 '16 at 23:36
  • zero, my reference to basic research comes straight from the way the StackExchange model is supposed to work; it's not some arbitrary or merely niggling criticism. If you have equal means, under the assumption of independent Poissons you have identical distributions. So testing if two Poissons come from different processes simplifies to testing means for equality. – Glen_b Mar 09 '16 at 23:38

0 Answers0