The discrete delta and nabla Mittag-Leffler distributions

Abstract

ABSTRACTIn 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.