Maximum Likelihood Estimation and Applications of the Weibull-Rayleigh Distribution

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.