On the moment generating functions for integer valued random variables

Abstract

In this note, we give explicit expressions of moment generating functions for integer valued random variables in both univariate and multivariate cases, which extend the results obtained by Nadarajah and Mitov [Communications in Statistics–Theory and Methods, 32, 2003, 47–60] and more recently by Chakraborti, Jardim and Epprecht [The American Statistician, 2017], Kwong and Nadarajah [Communications in Statistics–Theory and Methods, 2017]. Some examples are also discussed.

Keywords:

• high order moments
• integer valued random variable
• Moment generating function
• survival function

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• 62E

Acknowledgments

The authors express our gratitude to the two referees for their comments that led to an improved presentation of the article.

Additional information

Funding

Shaochen Wang is supported by the Fundamental Research Funds for the Central Universities (grant no. 2017BQ108).