Premium
Bivariate Modified Power Series Distribution Some Properties, Estimation and Applications
Author(s) -
Shoukri M. M.,
Consul P. C.
Publication year - 1982
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710240808
Subject(s) - mathematics , bivariate analysis , estimator , joint probability distribution , cartesian product , poisson distribution , series (stratigraphy) , power series , distribution (mathematics) , statistics , combinatorics , mathematical analysis , paleontology , biology
The class of bivariate modified power series probability distribution (BMPSD) has been defined by P(X = x, Y=y) =a(x, y) ( g (ϑ 1 ϑ 2 )) x ( h (ϑ 1 , ϑ 2 )) x where a(x,y) is a sub‐set of the Cartesian product of the set of non‐negative integers and g (ϑ 1 , ϑ 2 ), h (ϑ 1 ϑ 2 ) and f(ϑ 1 , (ϑ 1 , ϑ 2 ) are positive finite and successively differentiable functions of ϑ 1 and ϑ 2 . It includes a very large number of well known probability distributions. The recurrence relations for central moments and factorial moments have been determined. Also, the M.L. estimators for ϑ 1 and ϑ 2 and their asymptotic biases and variances are obtained. Some important properties are discussed. The results of an BMPSD have been applied to derive the corresponding results for the bivariate generalized negative bino‐mial distribution and the bivariate Lagrangian Poisson distribution.