Slash Maxwell Distribution: Definition, Modified Maximum Likelihood Estimation and Applications

Authors : Şükrü ACITAŞ, Talha ARSLAN, Birdal ŞENOĞLU

Pages : 249-263

Doi:10.35378/gujs.539929

View : 20 | Download : 7

Publication Date : 2020-03-01

Article Type : Research Paper

Abstract :In this study slash Maxwell insert ignore into journalissuearticles values(SM); distribution, defined as a ratio of a Maxwell random variate to a power of an independent uniform random variate, is introduced. Its stochastic representation and some distributional properties such as moments, skewness and kurtosis measures are provided. The maximum likelihood insert ignore into journalissuearticles values(ML); method is used for estimating the unknown parameters. However, closed forms of the ML estimators cannot be obtained since the likelihood equations include nonlinear functions of the unknown parameters. We therefore use Tiku`s insert ignore into journalissuearticles values(1967,1968); modified maximum likelihood insert ignore into journalissuearticles values(MML); methodology which allows to obtain explicit forms of the estimators. Some asymptotic properties of the MML estimators are derived. A Monte-Carlo simulation study is also carried out to compare the performances of the ML and MML estimators. Two data sets taken from the literature are modelled using the SM distribution in application part of the study. 
Keywords : Maxwell, Slashing methodology, Modified maximum likelihood, Stochastic representation, Modified maximum likelihood