A New Extended-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>X</mml:mi></mml:math>Family of Distributions: Properties and Applications
Zichuan Mi, Saddam Hussain, Anum Iftikhar, Muhammad Ilyas, Zubair Ahmad, Dost Muhammad Khan, Sadaf Manzoor
Abstract
During the past couple of years, statistical distributions have been widely used in applied areas such as reliability engineering, medical, and financial sciences. In this context, we come across a diverse range of statistical distributions for modeling heavy tailed data sets. Well-known distributions are log-normal, log-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mi>t</mml:mi></mml:math>, various versions of Pareto, log-logistic, Weibull, gamma, exponential, Rayleigh and its variants, and generalized beta of the second kind distributions, among others. In this paper, we try to supplement the distribution theory literature by incorporating a new model, called a new extended Weibull distribution. The proposed distribution is very flexible and exhibits desirable properties. Maximum likelihood estimators of the model parameters are obtained, and a Monte Carlo simulation study is conducted to assess the behavior of these estimators. Finally, we provide a comparative study of the newly proposed and some other existing methods via analyzing three real data sets from different disciplines such as reliability engineering, medical, and financial sciences. It has been observed that the proposed method outclasses well-known distributions on the basis of model selection criteria.