2016/08/23 by Huiming Zhang, Bo Li · 1 citation
Decision Sciences · Mathematics · Business, Management and Accounting · #Probability and Risk Models #Random Matrices and Applications #Advanced Queuing Theory Analysis
paper · doi:10.1080/03610926.2014.901375
openalex publication_date 2016/08/23 · openalex created_date 2025/10/10 · openalex updated_date 2025/11/06
The aim of this paper is to give some new characterizations of discrete compound Poisson distributions. Firstly, we give a characterization by the Lévy–Khintchine formula of infinitely divisible distributions under some conditions. The second characterization need to present by row sum of random triangular arrays converges in distribution. And we give an application in probabilistic number theory, the strongly additive function converging to a discrete compound Poisson in distribution. The next characterization, is an extension of Watanabe’s theorem of characterization of homogeneous Poisson process. The last characterization will be illustrated by waiting time distributions, especially the matrix-exponential representation.