ИСТИНА

It is well known the role of some discrete distributions such as Bernoulli, binomial, geometric, negative binomial, Poisson, Polya-Aeppli and others in applications of probability theory and mathematical statistics. We propose some variant of multivariate distribution whose components has a given univariate discrete distribution. In fact we consider some very general variant of so called reduction method. We find the explicit form of mass function and generating function of such distribution, investigate its properties. We prove that our construction is the unique in natural exponential families of distributions. Our results are the generalization and unification of many results of other authors. Also we consider some applications of these distributions in actuarial and financial mathematics and teletraffic theory.