A New Quantile Estimation Method of Weibull-Rayleigh Distribution
A. S. Ogunsanya *
Department of Statistics, University of Ilorin, Kwara, Nigeria.
E. E. E. Akarawak
Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria.
W. B. Yahya
Department of Statistics, University of Ilorin, Kwara, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
In this paper, we compared different Parameter Estimation method of the two parameter Weibull-Rayleigh Distribution (W-RD) namely; Maximum Likelihood Estimation (MLE), Least Square Estimation method (LSE) and three methods of Quartile Estimators. Two of the quartile methods have been applied in literature, while the third method (Q1-M) is introduced in this work. The methods have been applied to simulate data. These methods of estimation were compared using Error, Mean Square Error and Total Deviation (TD) which is also known as Sum Absolute Error Estimate (SAEE). The analytical results show that the performances of all the parameter estimation methods were satisfactory with data set of Weibull-Rayleigh distribution while degree of accuracy is determined by the sample size. The proposed quartile (Q1-M) method has the least Total Deviation and MSE. In addition, the quartile methods perform better than MLE for the simulated data. In particular, the proposed quartile methods (Q1-M) have an added advantage of simplicity in usage than MLE methods.
Keywords: Weibull-Rayleigh distribution, quartile estimator, least square estimator, maximum likelihood estimator, total deviation and bias.