COMPARISON BETWEEN BAYESIAN AND MAXIMUM LIKELIHOOD ESTIMATION OF SCALE PARAMETER IN WEIBULL DISTRIBUTION WITH KNOWN SHAPE UNDER LINEX LOSS FUNCTION

Abstract

Weibull distribution is widely employed in modeling and analyzing lifetime data. The present paper considers the estimation of the scale parameter of two parameter Weibull distribution with known shape. Maximum likelihood estimation is discussed. Bayes estimator is obtained using Jeffreys’ prior under linex loss function. Relative efficiency of the estimators are calculated in small and large samples for over-estimation and under-estimation using simulated data sets. It is observed that Bayes estimator fairs better especially in small sample size and when over estimation is more critical than under estimation.