The discrete delta and nabla Mittag-Leffler distributions

In this paper, we extend Bernstein theorem by using basic tools of calculus on time scales, and, as a further application of it, the discrete nabla and delta Mittag-Leffler distributions are introduced here with respect to their Laplace transforms on the discrete time scale. For these discrete distr...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2018-09, Vol.47 (18), p.4568-4589
Main Authors: Ganji, M., Gharari, F.
Format: Article
Language:English
Subjects:
Discrete Laplace transform
Laplace transforms
Mittag-Leffler distribution
moment generating function
time scale
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Summary:In this paper, we extend Bernstein theorem by using basic tools of calculus on time scales, and, as a further application of it, the discrete nabla and delta Mittag-Leffler distributions are introduced here with respect to their Laplace transforms on the discrete time scale. For these discrete distributions, infinite divisibility and geometric infinite divisibility are proved along with some statistical properties. The delta and nabla Mittag-Leffler processes are defined.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2017.1377254