Point estimates of parameters for Neuman distribution of order kстатья
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Дата последнего поиска статьи во внешних источниках: 4 февраля 2014 г.
Аннотация:We construct point estimates of the parameters of a Neuman distribution of order k as a representative
of the class of generalized Poisson distributions. The main properties of this distribution
(a recurrence formula, cumulants and moments, derivatives with respect to parameters) are
given in a system with infinitely many parameters, and the relationships are demonstrated with
the previously obtained expressions in a two-parameter system. Among the point estimation
methods we consider the moment method and the substitution method, which both lead to simple
systems of equations; the solvability conditions for these systems are investigated. The efficiency
of the estimators relative to the Cramer – Rao lower bound is examined and some conclusions
are drawn regarding their applicability. The equations of the maximum likelihood estimation
method are written out for infinitely many parameters and for the two-parameter case.