Contributions Towards New Families of Distributions: An Investigation, Further Developments, Characterizations and Comparative Study

Abstract

In the past couple of years, statistical models have been extensively used in applied areas for analyzing real data sets. However, in numerous situations, the traditional distributions are not flexible enough to cater to different aspects of the real phenomena. For example, (i) in the practice of reliability engineering and biomedical analysis, some distributions provide the best fit to the data having monotonic failure rate function, but fails to provide the best fit to the data having non-monotonic failure rate function, (ii) some statistical distributions provide the best fit for small insurance losses, but fails to provide an adequate fit to large claim size data, and (iii) some distributions do not have closed forms causing difficulties in the estimation process. To address the above issues, therefore, several methods have been suggested to improve the flexibility of the classical distributions. In this article, we investigate some of the former methods of generalizing the existing distributions. Further, we propose nineteen new methods of extending the classical distributions to obtain flexible models suitable for modeling data in applied fields. We also provide certain characterizations of the newly proposed families. Finally, we provide a comparative study of the newly proposed and some other existing well-known models via analyzing three real data sets from three different disciplines such as reliability engineering, medical, and financial sciences.