Maximum Likelihood Estimation and Applications of the Weibull-Rayleigh Distribution

  • Eno Akarawak Department of Mathematics, University of Lagos, Lagos, Nigeria.
  • Ismail Adeleke Department of Actuarial Science and Insurance, University of Lagos, Akoka (Nigeria)
  • Ray Okafor Department of Mathematics, University of Lagos, Lagos, Nigeria.
Keywords: Weibull-Rayleigh distribution, Weibull distribution, Rayleigh distribution, Weibull-X family, Maximum Likelihood method.

Abstract

Recently, the Weibull-Rayleigh Distribution (WRD) has been derived as a new class of the Weibull-X family of distributions and expressions for some of its distributional properties defined and studied. Further to these, this article employs the method of maximum likelihood to find estimators for parameters of the Weibull-Rayleigh distribution. The method of maximum likelihood yielded a closed form estimator for the scale parameter but
cannot produce a closed form estimator for the shape parameter of WRD. Some properties of the estimator of the scale parameter are discussed. Two numerical data sets on insurance claims and marriage survival time are used to illustrate the applicability of the method of maximum likelihood of the Weibull-Rayleigh Distribution.

Published
2018-04-12
How to Cite
Akarawak, E., Adeleke, I., & Okafor, R. (2018). Maximum Likelihood Estimation and Applications of the Weibull-Rayleigh Distribution. International Journal of Mathematical Sciences and Optimization: Theory and Applications, 2017, 233 - 249. Retrieved from http://ijmso.unilag.edu.ng/article/view/11
Issue
Vol 2017
Section
Articles

This is an Open Access article distributed under the terms of the Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, adaptation, and reproduction in any medium, provided that the original work is properly cited.