Estimating the Shape Parameter of the Exponential-Weibull Distribution using Bayesian Technique
Faith Nick Duru, Sani Doguwa Ibrahim, Jamilu Garba
Keywords: Exponential-Weibull Distribution; Bayesian technique; Maximum likelihood method; Informative and non-informative priors; Loss function; Means square error
Abstract
The Exponenial-Weibull Distribution (EWD) has been found to be useful in modeling and prediction of real life events. Its three parameter property makes it more flexible in modeling/accommodating dataset of different characteristics. However, Bayesian techique which is more robust and efficient in most cases, has not been used to estimate the shape parameter of this very important distribution. In view of this, Bayesian technique has been employed to estimate the shape parameter of the distribution. The performance of the technique is assessed and compared with that of maximum likelihood using Monte-carlo simulation. One informative and two non-informative priors as well as three loss functions were used for the study. The results showed that; Bayesian technique produced estimators with lower MSEs regardless of the chosen sample size and parameter value.