A new skew logistic distribution: Properties and applications

Abstract

Following the methodology of Azzalini, researchers have developed skew logistic distribution and studied its properties. The cumulative distribution function in their case is not explicit and therefore numerical methods are employed for estimation of parameters. In this paper, we develop a new skew logistic distribution based on the methodology of Fernández and Steel and derive its cumulative distribution function and also the characteristic function. For estimating the parameters, Method of Moments, Modified Method of Moment and Maximum likelihood estimation are used. With the help of simulation study, for different sample sizes, the parameters are estimated and their consistency was verified through Box Plot. We also proposed a regression model in which probability of occurrence of an event is derived from our proposed new skew logistic distribution. Further, proposed model fitted to a well studied lean body mass of Australian athlete data and compared with other available competing distributions.