The Performance Evaluation of Nine Methods for the Estimation of Weibull Distribution Parameters

Abstract

In this paper, a report on the different methods for estimation of the parameter of the Weibull 2-parameter distribution is presented. The nine approaches were compared in terms of their fits using the statistical criteria (analysis of variance (ANOVA), model of' selection criterion (MSC), Coefficient of Determination (CD), Correlation coefficient (R) and Akaike Information Criterion (AIC)) to select the best method.  The study revealed that mean rank is the best method among the methods in the graphical and analytical procedures. Numerical simulation studies carried out show that the maximum likelihood estimation method significantly outperformed other methods based on the MSC, CD, R and AIC. The values for the parameters in the Weibull 3-parameter were 1.316, 105.425 mm/h and 0.293 for α, β and λ respectively. The values of  MSC, CD AIC and R were 1.853 and 1.453, 0.860 and 0.802, 211.891 and 295.978, and 0.927 and 0.895 for Weibull 2 and 3 – parameters respectively.  It was concluded that mean rank, symmetric, Lysen and Moment methods are the best based on the values of MSC, CD and R. Care must be taken in selecting MLM, graphical and least square methods for Weibull distribution parameters determined based on the lower values of MSC, CD and R as well as higher values of AIC.