The Weighted Exponentiated Family of Distributions: Properties, Applications and Characterizations

In this paper a new method of introducing an additional parameter to a continuous distribution is proposed, which leads to a new class of distributions, called the weighted exponentiated family. A special sub-model is discussed. General expressions for some of the mathematical properties of this class such as the moments, quantile function, generating function and order statistics are derived; and certain characterizations are also discussed. To estimate the model parameters, the method of maximum likelihood is applied. A simulation study is carried out to assess the finite sample behavior of the maximum likelihood estimators. Finally, the usefulness of the proposed method via two applications to real data sets is illustrated.