ИСТИНА

The generalized negative binomial distribution (GNB) is a new wide and flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma distributions. This family of discrete distributions is very wide and embraces Poisson distributions, negative binomial (Polya) distributions including geometric distributions, Sichel distributions, Weibull-Poisson distributions and many other types of distributions supplying descriptive statistics with many flexible models. These distributions seem to be very promising for the statistical description of many real phenomena being very convenient and almost universal models. For example, GNB distributions can be successfully applied to modeling statistical regularities in duration of specific periods in data. The problem of statistical estimation of the parameters of GNB distributions is extremely complicated. To find estimations, the two-stage grid EM algorithm for the GNB distribution can be used. The paper presents an alternative methodology based on the method of finding the best distribution using minimization of few distances in special spaces. It allows to obtain parameter estimates without using grid methods.