Asymptotic results for families of random variables having power series distributions
Volume 9, Issue 2 (2022), pp. 207–228
Pub. online: 3 February 2022
Type: Research Article
Open Access
Open Access
Received
13 September 2021
13 September 2021
Revised
6 December 2021
6 December 2021
Accepted
25 December 2021
25 December 2021
Published
3 February 2022
3 February 2022
Abstract
Suitable families of random variables having power series distributions are considered, and their asymptotic behavior in terms of large (and moderate) deviations is studied. Two examples of fractional counting processes are presented, where the normalizations of the involved power series distributions can be expressed in terms of the Prabhakar function. The first example allows to consider the counting process in [Integral Transforms Spec. Funct. 27 (2016), 783–793], the second one is inspired by a model studied in [J. Appl. Probab. 52 (2015), 18–36].
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