A Note on the Modes of the Poisson Distribution of Order k
Probability
2013-12-30 v1 Statistics Theory
Statistics Theory
Abstract
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.
Keywords
Cite
@article{arxiv.1312.7139,
title = {A Note on the Modes of the Poisson Distribution of Order k},
author = {Andreas N. Philippou},
journal= {arXiv preprint arXiv:1312.7139},
year = {2013}
}
Comments
3 pages