Some Classes Of Distributions On The Non-Negative Lattice

A method for constructing distributions on the non negative integers as discrete analogue of continuous distributions on the non negative real is presented. A justification of the definition of discrete self decomposable laws is provided. Discrete analogue of distributions of the same type and the role of Bernoulli law in this context is discussed. Generalizations of some discrete laws and their properties are given. The geometric compounding problem for discrete distributions is studied by introducing discrete semi Mittag Leffler laws.