Last Friday, I had to submit a homework which required me to evaluate $\Pr(A > B)$ and $\Pr(A = B)$, where $A$ and $B$ were two independent Poisson random variables with parameters $\alpha$ and $\beta$ respectively.
I then started evaluating the sum.
Then I was stuck. I couldn’t compute this sum also.
I googled for a solution for hours, and after I saw equation (3.1) in a paper, I gave up finding exact solutions.1 As a supporter of free software, I avoided using M$ Ex*, and wrote a program in C++ to approximate the above probabitities by directly adding them term by term.
Assume that Poisson r.v. A and B are indepedent Parameter for A: 1.6 Parameter for B: 1.4 Number of terms to be added (100 <= N <= 1000): 8 P(A > B) = 0.423023, P(A < B) = 0.335224, P(A = B) = 0.241691
A one-line method for writing the content of a function which returns the factorial of a number.
Evaluation of a function inside GDB
Keller, J. B. (1994). A characterization of the Poisson distribution and the probability of winning a game. The American Statistician, 48(4), 294–298. ↩