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In this article, we introduce a new general family of distributions. The submodels of the general family accommodate various shapes of pdf and hazard rate, involving decreasing, increasing, bathtub and J-shapes. Hence, it can provide analysis for many practical datasets. Mathematical expressions for the family are obtained, including moments, moment generating and quantile functions, stochastic ordering, and entropy. Some submodels of the family are inserted based on the baseline distributions: Exponential, Gompertz, Lindley, and weight exponential distributions. Estimation of the model parameters is justified by the method of maximum likelihood. Capability of the family is shown by fitting three practical datasets to the mentioned submodels.
Bakouch et al. (2020) studied this question.