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Exponentiated Odd Weibull Distribution, Simulation Study, Vuong Test, Empirical Distribution Function, Shapiro-Wilk W-test.

In this paper, three-parameter Weibull extensions: generalized gamma (GG), exponentiated Weibull (EW), and Odd Weibull (OW) distributions, which are capable of modeling data that exhibit five major hazard shapes, are compared using Vuong, empirical distribution function, and Shapiro-Wilk W- tests. The goal of this work is to compare the GG, EW, and OW distribution using better model selection criteria under general conditions as addressed by the Voung test, in addition to the tests considered. Our simulation study and graphical analysis show that the OW distribution is different from both GG and EW distributions even though all three distributions have five common hazard shapes. An example using voltage data is also considered to illustrate applications of the three distributions. Our comparative results led us to develop a six-parameter generalized distribution which is an extension of the GG, EW, and OW distributions. A four-parameter sub-model of this distribution, the exponentiated Odd Weibull distribution which has applications in modeling lifetime data, was studied in our recent publication.