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

Şükrü ACITAŞ, Talha ARSLAN, Birdal ŞENOĞLU
2020 GAZI UNIVERSITY JOURNAL OF SCIENCE  
Highlights • A new distribution is studied. • Parameters of the distribution are estimated using the MML methodology. • Explicit forms of the MML estimators are provided. Article Info Abstract In this study slash Maxwell (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
more » ... . The maximum likelihood (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 (1967 Tiku's ( ,1968 modified maximum likelihood (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.
doi:10.35378/gujs.539929 fatcat:rvvn7ayezbbk5jiizhisqlfdje