SOME CLASSES OF DISTRIBUTIONS ON THE NON-NEGATIVE LATTICE

A method for constructing distributions on the non-negative lattice of points Io = {0,1,2, ….} as discrete analogue of continuous distributions on [0,∞ ) is presented. A justification of the definition of discrete class-L 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 distributions and properties of α -Poisson laws are given. The geometric compounding problem for discrete distributions is studied by introducing discrete semi Mittag-Leffler laws.