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


Acitas S., Arslan T. , ŞENOĞLU B.

GAZI UNIVERSITY JOURNAL OF SCIENCE, vol.33, no.1, pp.249-263, 2020 (Journal Indexed in ESCI) identifier

  • Publication Type: Article / Article
  • Volume: 33 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.35378/gujs.539929
  • Title of Journal : GAZI UNIVERSITY JOURNAL OF SCIENCE
  • Page Numbers: pp.249-263

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 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 (1967,1968) 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.