A note on the modes of the negative binomial distribution of order k, type I
Probability
2017-02-09 v1
Abstract
Upper and lower bounds are derived for the mode(s) of the negative binomial distribution of order k, type I, with parameters r and p, which are employed to establish an explicit formula for the mode(s) in terms of r and k when p equals 0.5. It is also shown as a direct consequence of the upper bound alone that the mode is k when r equals 1. The derivation of the bounds is based on a known recurrence relation satisfied by the probability mass function of the distribution.
Keywords
Cite
@article{arxiv.1702.02183,
title = {A note on the modes of the negative binomial distribution of order k, type I},
author = {Costas Georghiou and Andreas N. Philippou and Zaharias M. Psillakis},
journal= {arXiv preprint arXiv:1702.02183},
year = {2017}
}
Comments
7 pages