The average of a negative-binomial Lévy process and a class of Lerch distributions

Weixuan Xia

Communications in Statistics - Theory and Methods, 2020, vol. 49, issue 4, 1008-1024

Abstract: In this paper we discuss the average of a Lévy process with a marginal negative-binomial distribution taken over a finite time interval, and simultaneously introduce a new class of absolutely continuous distribution based on Lerch’s transcendent. Various distribution formulas are obtained in explicit form, including characteristic functions, distribution functions and moments. Some interesting asymptotics are also analyzed. As a consequence, we obtain rapidly converging series representations for the probability distribution of the average process. Numerical examples are provided in order to illustrate the proposed formulas.

Date: 2020
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DOI: 10.1080/03610926.2018.1554135

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