The Marshall-Olkin extended inverted Kumaraswamy distribution: Theory and applications

Abstract

A new three parametric distribution is proposed and analyzed, termed as the Marshall-Olkin extended inverted Kumaraswamy (MOEIK) distribution. This generalization has some renowned sub models such as the Beta type II, the Lomax and the Fisk distribution, stated in literature. Study includes the basic properties of the observed probabilistic model. Explicit expressions for major mathematical properties of this distribution such as quantile function, complete and incomplete moments, entropies and moments of order statistic are derived. Maximum likelihood estimation method is used to estimate the parameters. For different parameter values, a number of simulation studies are conducted for different sample sizes and compare the performance of the MOEIK distribution. Three real life applications are provided to explain the potentiality and reliability of the extended distribution with confidence that the generalized model have wider applications in hydrology and the associated fields. Keywords: Inverted Kumaraswamy distribution, Quantile function, Moment generating function, Order statistic, Maximum likelihood