Elementary expressions for moments of truncated negative binomial random variables

ABSTRACT

Moments of truncated negative binomial random variables arise in many areas. But moments of general order do not appear to be available, even a correct expression for the variance of a truncated negative binomial random variable was derived only in 2016. Here, we derive the elementary expressions for the moments of general order for four different types of truncated negative binomial random variables. Computational issues are discussed for the expressions.

KEYWORDS:

• Lerch function
• Maple
• Stirling number of the first kind.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E99

Acknowledgments

The authors would like to thank the referee and the editor for careful reading and comments which greatly improved the article.