The Exponentiated Generalized Alpha Power Exponential Distribution: Properties and Applications

In this paper, we first introduce the exponentiated generalized alpha power family of distributions to extend several other distributions. We use the new family and develop a new distribution, called the exponentiated generalized alpha power exponential (EGAPEx) distribution. The proposed EGAPEx distribution provides greater flexibility in modeling data from a practical point of view. The new model includes the exponential; alpha power exponential; alpha power generalized exponential, generalized exponential, standardized generalized exponential and exponentiated generalized exponential distributions as a special cases. This distribution exhibits four hazard rate shapes such as L shaped, increasing, decreasing, and upside-down bathtub. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by maximum likelihood, maximum product spacing, and Bayesian estimation methods. In addition, we have obtained approximate confidence intervals, two bootstrap confidence intervals, and Bayes credible intervals. A Monte Carlo Simulation is performed to compare the different methods of estimation. We illustrate the performance of the proposed distribution through two real data sets; one is related to economic data and another is failure time data and the data sets show the proposed distribution is superior in its ability to model the data sets as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions.