Andreas N. Philippou
Published 2013-12-26Version 1
It is shown that for any positive integer k and positive parameter lambda less than 2/k(k+1), the Poisson distribution of order k with parameter lambda has a unique mode, 0. In addition, the Poisson distribution of order 2 has a unique mode, 0, if lambda is less than -1 plus the square root of 3. It has two modes, 0 and 2, if lambda is equal to -1 plus the square root of 3, and it has a unique mode, 2, if lambda is greater than -1 plus the square root of 3 and less than 1.
Scaling behavior for the median of the Poisson distribution of order $k$
Alternative combinatorial sum for the probability mass function of the Poisson distribution of order $k$
Entropies of the Poisson distribution as functions of intensity: "normal" and "anomalous" behavior
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