Creation of New Univariate Distributions: A Novel Reduction Method From a Bivariate Distribution Family

Abstract

Since some of the classical distributions fail to model data in statistics, necessity of having new distributions arises. Accordingly, studies about expanding well-known distribution families are increasing nowadays. In this paper, bivariate Ali-Mikhail-Haq copula family is reduced to univariate and under which conditions obtained distributions become a distribution function is investigated. Characteristics of these reduced distributions are reviewed, and parameter estimation is done with the help of various estimation methods. The new distributions obtained by reducing bivariate or multivariate distributions to univariate are seen as more flexible than basic distributions. This flexibility leads us to think that use of this distribution for modelling different data sets and using them in various fields may be favourable. Therefore, our motivation for this article was to propose a method for reducing bivariate copulas to univariate, which has not been used in literature before. So that, wide range of use will be provided for modelling various data with this new method. The superiorities of the distributions used to model real data sets in the literature before and the newly proposed distributions are compared and evaluated in application.