2023/10/12 by Mane, S. R.
#05-08 #11B37 #39B05 #60E05 #Combinatorics (math.CO) #FOS: Mathematics #Probability (math.PR)
paper · doi:10.48550/arxiv.2310.08615
Kostadinova and Minkova published an expression for the probability mass function (pmf) of the Poisson distribution of order k, as a combinatorial sum (Pliska~Stud.~Math.~Bulgar. \bf 22, 117-128 (2013)). Inspired by their elegant solution, this note presents an alternative combinatorial sum for the pmf of the Poisson distribution of order k. The terms are partitioned into blocks of length k (as opposed to k+1 by Kostadinova and Minkova). The new sum offers an advantage in the following sense. For n∈[rk+1,(r+1)k], the lowest power of λ in the pmf is λr+1. Hence the lower limit of summation can be increased, to avoid needlessly calculating terms which cancel to identically zero.