ON MARSHALL – OLKIN TECHNIQUE OF EXTENDING UNIVARITE DISTRIBUTIONS

Abstract

problems of establishing and extending new classes and families of discrete and continuous probability distributions are one of the most important research topics in the theory of distributions. The Kotz and Vicari (2005) gave highlights the most important early developments of statistical distributions. Since 1980, research methods have begun to generate new distributions that tend to add new parameters to known statistical distributions. This is probably due to the mathematical and analytic capabilities available in software such as R (packages), Matlabm, Mable and Mathemahca, through which researchers can easily tackle problems with incomplete beta and gamma functions in generalized family. The second reason lies in the characteristics of the curved tail of the new statistical distribution produced by adding one or more parameters to old distribution. Thirdly, this parameters (s) induction has also proved to be helpful In improving the goodness of fit of the proposed family of distribution.