Alpha power inverted Kumaraswamy distribution: Definition, different estimation methods, and application

Abstract

In this study, an alpha power inverted Kumaraswamy (APIK) distribution is introduced. The APIK distribution is de- rived by applying alpha power transformation to an inverted Kumaraswamy distribution. Some submodels and limiting cases of the APIK distribution are obtained as well. To the best of the authors’ knowledge, some of these distributions have not been introduced yet. Statistical inference of the APIK distribution, including survival and hazard rate func- tions, are obtained. Unknown parameters of the APIK distribution are estimated by using the maximum likelihood (ML), maximum product of spacings (MPS), and least squares (LS) methods. A Monte Carlo simulation study is con- ducted to compare the efficiencies of the ML estimators of the shape parameters α, β and λ of the APIK distribution with their MPS and LS counterparts. An application to a real data set is provided to show the implementation and modeling capability of the APIK distribution.