Alpha Power Inverted Kumaraswamy Distribution: Definition, Different Estimation Methods and Application

Abstract

In this study, an alpha power inverted Kumaraswamy distribution having three shape parameters is obtained by applying the alpha power transformation to the inverted Kumaraswamy distribution. Then, its survival and hazard rate functions are expressed in closed forms. Some of its submodels and limiting cases are provided as well. Its parameters are estimated by using the maximum likelihood, maximum product of spacings, and least squares methods. A Monte-Carlo simulation study is conducted to show the performances of the considered estimation methods. An application to a real data set including values of breaking stress of carbon fibers is provided to illustrate an implementation of the proposed distribution and its modeling capability. The results show that alpha power inverted Kumaraswamy distribution can be an alternative to the its rivals.