Statistical Properties and Applications of the Exponentiated Chen-G Family of Distributions: Exponential Distribution as a Baseline Distribution

Abstract

In this work, the Exponentiated Chen-G family of distributions is studied by generalizing the Chen-G family of distributions through the introduction of an additional shape parameter. The mixture properties of the derived family are studied. Some statistical properties of the family were considered, including moments, entropies, moment generating function, order statistics, quantile function. The estimation of the parameters of the family of distributions was done using the maximum likelihood estimation method, considering complete and censored situations. Using the Exponential distribution as a baseline, the Exponentiated Chen Exponential distribution was obtained and its statistical properties were studied. The Exponentiated Chen Exponential distribution has the Exponentiated Exponential, Exponential, Chen Exponential distributions as submodels. Lastly, the Exponentiated Chen Exponential distribution was applied to two real data sets and the results were compared with its submodels and relative distributions.