A Generalized Stochastic Process for Count Data

21 Pages Posted: 25 Jul 2014

See all articles by Li Zhu

Li Zhu

Georgetown University

Kimberly F. Sellers

Georgetown University - Department of Mathematics and Statistics

Galit Shmueli

Institute of Service Science, National Tsing Hua University, Taiwan

Date Written: July 23, 2014

Abstract

The Bernoulli and Poisson are two popular discrete count processes; however, both rely on strict assumptions that motivate their use. We instead propose a generalized count process (the Conway-Maxwell-Poisson process) that not only includes the Bernoulli and Poisson processes as special cases, but also serves as a flexible mechanism to describe count processes that approximate data with over- and under-dispersion. We introduce the process and its associated generalized waiting time distribution with several real-data applications to illustrate its flexibility for a variety of data structures.

Keywords: Bernoulli process, Poisson process, count process, waiting time, dispersion, dependence, Conway-Maxwell-Poisson (COM-Poisson)

Suggested Citation

Zhu, Li and Sellers, Kimberly F. and Shmueli, Galit, A Generalized Stochastic Process for Count Data (July 23, 2014). Available at SSRN: https://ssrn.com/abstract=2470803 or http://dx.doi.org/10.2139/ssrn.2470803

Li Zhu

Georgetown University ( email )

Washington, DC 20057
United States

Kimberly F. Sellers (Contact Author)

Georgetown University - Department of Mathematics and Statistics ( email )

United States
202-687-8829 (Phone)

HOME PAGE: http://www9.georgetown.edu/faculty/kfs7

Galit Shmueli

Institute of Service Science, National Tsing Hua University, Taiwan ( email )

Hsinchu, 30013
Taiwan

HOME PAGE: http://www.iss.nthu.edu.tw

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