It is well known that the Poisson distribution with parameter λ (>0) has a unique mode [λ] if λ is not a positive integer and two modes λ and λ-1 if λ is a positive integer. It is also known that the Poisson distribution of order k (k = 1, 2, …) with parameter λ (>0) has a unique mode 0 if 0 < λ 0) has a unique mode 0 if 0 < λ < sr3 – 1. It has two modes 0 and 2 if λ = sr3 – 1, and it has a unique mode 2 if sr3 – 1 < λ < 1.

For all other values of k and λ the modes of the Poisson distribution of order k are unknown.

Article A Note on the Modes of the Poisson Distribution of Order k