A GENERAL MATHEMATICAL AND STATISTICAL MODEL

Print ISSN: 2319-1023

Abstract

A general model in the elliptically contoured family of functions and under the idea of a pathway model is introduced here. Through a pathway parameter b one will be able to go from one family of functions to two other families of functions, thus three different families of functions. A standard form of the model belongs to spherically symmetric family of functions. As particular cases and applications, it is shown that some real multivariate extensions of the basic models of generalized type-1 beta, type-2 beta, gamma, chisquare, Student-t, F, Cauchy, Maxwell-Boltzmann, Raleigh, Gaussian and related densities are available from the general model introduced. Reliability analysis concepts are introduced for the multivariate cases and some properties of the general model are also discussed. Then the model is extended to the complex multivariate case. In the complex case also, various connections and applications are pointed out.

Keywords and Phrases

Multivariate distributions, ellipsoid of concentration, random volumes, multivariate reliability analysis, generalized entropy optimization, generalized Gaussian, Maxwell-Boltzmann, Raleigh distributions, H-function.

A.M.S. subject classification

15A04, 15B52, 26B10, 62E15.

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