The discrete delta and nabla Mittag-Leffler distributions

ABSTRACT

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.

KEYWORDS:

• Discrete Laplace transform
• Mittag-Leffler distribution
• moment generating function
• time scale.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 93C70
• 26A33
• 39A12

Acknowledgments

The authors would like to acknowledge the comments and suggestions of both the referees which led to substantial improvement of the manuscript.