  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.
