The generalized negative binomial distribution (GNB) is a new flexible family
of discrete distributions that are mixed Poisson laws with the mixing
generalized gamma (GG) distributions. This family of discrete distributions is
very wide and embraces Poisson distributions, negative binomial 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. GG distributions are widely applied in signal and image
processing and other practical problems. The statistical estimation of the
parameters of GNB and GG distributions is quite complicated. To find estimates,
the methods of moments or maximum likelihood can be used as well as two-stage
grid EM-algorithms. The paper presents a methodology based on the search for
the best distribution using the minimization of â„“p-distances and
Lp-metrics for GNB and GG distributions, respectively. This approach, first,
allows to obtain parameter estimates without using grid methods and solving
systems of nonlinear equations and, second, yields not point estimates as the
methods of moments or maximum likelihood do, but the estimate for the density
function. In other words, within this approach the set of decisions is not a
Euclidean space, but a functional space.Comment: 13 pages, 6 figures, The XXI International Conference on Distributed
Computer and Communication Networks: Control, Computation, Communications
(DCCN 2018