A New Method for Generating Discrete Analogues of Continuous Distributions (original) (raw)

In this paper we use discrete fractional calculus for showing the existence of delta and nabla discrete distributions and then apply time scales for definition of delta and nabla discrete gamma distributions. The main result of this paper is unification of the continuous and discrete gamma distributions, which is at the same time a distribution to so-called time scale. Also, starting from the Laplace transform on time scales, we develop concept of moment generating function for these distributions.