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In this paper, we introduce the exponentiated generalized alpha power family of distributions to extend the several other distributions. We used the new family to discuss the exponentiated generalized alpha power exponential (EGAPEx) distribution. Some statistical properties of the EGAPEx distribution are obtained. The model parameters are obtained by the maximum likelihood estimation (MLE), maximum product spacing (MPS) and Bayesian estimation methods. A Monte Carlo Simulation is performed to compare between different methods. We illustrate the performance of the proposed new family of distributions by means of two real data sets and the data sets show the new family of distributions is more appropriate as compared to the exponentiated generalized exponential, alpha power generalized exponential, alpha power exponential, generalized exponential and exponential distributions.
El-Sherpieny et al. (2022) studied this question.