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American Journal of Theoretical and Applied Statistics
American Journal of Theoretical and Applied Statistics (AJTAS) publishes papers developing and analyzing new methods for any field of statistics. It is expected that the papers give interesting and novel contributions to statistical theory and its applications at a good mathematical level. The results should be presented in form of theorems together with their mathematical proofs, which should not be merely routine calculations. Additionally, a discussion of the results and their value for the theory or for applications could be a valuable addition, as well as numerical results on the efficiency or examples for the applicability of the theoretical results.

ISSN:2326-8999 (Print)

ISSN:2326-9006 (Online)

Article Information
On Nonnegative Integer-Valued Lévy Processes and Applications in Probabilistic Number Theory and Inventory Policies

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Authors
[01]
Huiming Zhang, Dept. of Mathematics and Statistics, Central China Normal University, Wuhan, China
[02]
Jiao He, Dept. of Mathematics and Statistics, Central China Normal University, Wuhan, China
[03]
Hanlin Huang, Dept. of Mathematics and Statistics, Central China Normal University, Wuhan, China

To cite this article
Huiming Zhang, Jiao He, Hanlin Huang, On Nonnegative Integer-Valued Lévy Processes and Applications in Probabilistic Number Theory and Inventory Policies, American Journal of Theoretical and Applied Statistics. Vol. 2, No. 5, 2013, pp. 110-121. doi: 10.11648/j.ajtas.20130205.11

Abstract
Discrete compound Poisson processes (namely nonnegative integer-valued Lévy processes) have the property that more than one event occurs in a small enough time interval. These stochastic processes produce the discrete compound Poisson distributions. In this article, we introduce ten approaches to prove the probability mass function of discrete compound Poisson distributions, and we obtain seven approaches to prove the probability mass function of Poisson distributions. Finally, we discuss the connection between additive functions in probabilistic number theory and discrete compound Poisson distributions and give a numerical example. Stuttering Poisson distributions (a special case of discrete compound Poisson distributions) are applied to numerical solution of optimal (s, S) inventory policies by using continuous approximation method.

Keywords
Probability Mass Function, Nonnegative Integer-Valued Lévy Processes, Probabilistic Number Theory, Discrete Compound Poisson Distribution, (S, S) Inventory Policies

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