New alpha power unit distribution: properties and application

In this article, an absolutely continuous two parameter alpha power unit (APU, in short) probability model is introduced using the method of adding an extra parameter developed originally by Mahdavi and Kundu [A new method for generating distributions with an application to exponential distribution, Comm. Stat. Theory Methods 46 (2017), pp. 6543-6557]. The derived probability model appears to be more flexible than some of the existing well-known univariate distributions defined on the unit interval due to its variety of shapes of the hazard function. Several useful structural properties of the APU distribution are discussed, including quantile function, residual life function, moments, stochastic ordering and order statistics. The maximum likelihood estimators of unknown parameters cannot be obtained in explicit forms, and they have to be obtained by solving non-linear equations only. A simulation study has been conducted to check the consistency of the adopted MLE procedure. Two real-life data sets have been re-analyzed to show how the proposed probability model works in practice.