Abstract
This paper proposes a member of the T-X family that incorporates heavy-tailed distributions, known as "a new exponential-X family of distribution." As a special case, the paper studies a submodel of the proposed class named a "new exponential Weibull (NEx-Wei) distribution." Some mathematical properties including hazard rate function, ordinary moments, moment generating function, and order statistics are discussed. Furthermore, we adopt the method of MLE (maximum likelihood estimation) for estimating its model parameters. A brief Monte Carlo simulation study is conducted to evaluate the performances of the MLEs based on biases and mean square error. Finally, we provide a comprehensive study to illustrate the introduced approach by analyzing three real data sets from different disciplines. The analytical goodness of fit measure of the proposed distribution is compared with other well-known distributions. We hope that the proposed class may produce many more new distributions for fitting monotonic and nonmonotonic data in the field of reliability analysis and survival analysis as well.