Alpha-power power distribution

Abstract

Background & Aim: Due to the applicability of the statistical distributions in many areas of sciences, adding parameters to an existing distribution for developing more flexible models have been overlooked in the statistical literatures. Methods & Materials: A new generalization of power distribution is proposed using alpha power transformation method. The new distribution is more flexible than the power distribution and contains distributions that can be unimodal or right skewed. Results: We study some statistical properties of the new distribution, including mean residual lifetime, quantiles, mode, moments, moment generating function, order statistics, some entropies and maximum likelihood estimators. Conclusion: We fit the APP and some competitive models to one real data set and show that the new model has a superior performance among the compared distributions as evidenced by some goodness-of fit statistics.

Keywords

• Alpha-power transformation
• Hazard rate function
• Maximum likelihood estimation
• Power distribution
• Survival function