Affiliation:
1. Department of Mathematics, University of Central Arkansas, Conway, AR 72035, USA
2. Department of Mathematics, University of Patras, 26500 Patras, Greece
Abstract
In this article, new properties of the Poisson distribution of order k with parameter λ are found. Based on them, the modes of the Poisson distributions of order k=3 and 4 are derived for λ in (0,1). They are 0, 3, 5, and 0, 4, 7, 8, respectively, for λ in specified subintervals of (0, 1). In addition, using Mathematica, computational results for the modes of the Poisson distributions of order k=2,3, and 4 are presented for λ in specified subintervals of (0,2).
Subject
General Physics and Astronomy
Reference28 articles.
1. Waiting for the k-th consecutive success and the Fibonacci sequence of order k;Philippou;Fibonacci Q.,1982
2. A generalized geometric distribution and some of its properties;Philippou;Stat. Probab. Lett.,1983
3. Poisson and compound Poisson distributions of order k and some of their properties;Philippou;Zap. Nauchnykh Semin. LOMI,1983
4. The negative binomial distribution of order k and some of its properties;Philippou;Biom. J.,1984
5. Philippou, A.N. (1986). Fibonacci Numbers and Their Applications, Reidel.