A Comparison of Methods of Estimating the Parameters of the Three-Parameter Weibull Distribution with Application to Reliability Analysis

In this work, eight methods of estimating the parameters of a three-parameter Weibull distribution were discussed and compared. The methods are; method of moments (MOM), maximum likelihood method (MLE), percentile method (PM), method of L-moments (LM), Teimouri and Gupta Beta (MGB), maximum product of spacing method (MPS), modified method of moments (MMM) and the Goda’s polynomial method (GPM). A simulation study was carried out were samples of different sizes with different shape parameter ( ) values were generated and the five methods were applied to the samples. The ischolar_main means square error (RMSE) was the basis for comparison of the methods based on their ability to estimate each parameter accurately. The Euclidean norm was also used to compare performance of methods based on their ability to accurately estimate the three parameters. The results show that the Mahdi and Gupta method is the best method for estimating the parameters of a three-parameter Weibull distribution in almost all the simulation conditions.  The maximum product of spacing performed second best. It was also discovered that sample size does not really affect the choice of method but the accuracy of all the methods increases with sample. An application of these methods to real life data was also demonstrated here.