Modified Frechet distributions and their generalized families

Abstract

The Frechet distribution is used for modeling extreme events. There are different approaches to developing statistical distributions which include  the use of translation methods, system of differential equations, quantile methods among others. Existing statistical distributions are also modified  or generalized to accommodate other different types of data and improve goodness of fit to data. Addition of extra parameter(s) is one approach  used for generalizing existing distributions such that the base distributions are embedded in the new generalized distributions. Some methods of  parameter induction were used to obtained families of generalized distributions. Parameter(s) were also introduced into the probability  distributions of the Frechet distribution to derive functions of its modified versions belonging to each of the generalized families derived. Further  study is recommended on some of the modified Frechet distributions and their generalized families.