A Generalized Mixture of standard Logistic and skew Logistic distributions: Properties and applications

Abstract

In this paper, the generalized mixture of standard logistic and skew logistic is introduced as a new class of distribution. Some important mathematical properties of this novel distribution are discussed along with a graphical presentation of the density function. These properties include moment generating function, $m^{th}$ order moment, mean deviation, characteristic function, entropy, among others. Moreover, a location scale type extension of the proposed distribution is considered, and the maximum likelihood estimation method for this model is presented. To examine the performance of the estimated parameters of the proposed distribution, a simulation study is also conducted using the rejection sampling method. Furthermore, an application using two real-life data sets are also illustrated. Finally, the likelihood ratio test is performed to study the discrepancies between proposed model with their counterparts.