New closed-form efficient estimators for a bivariate Weibull distribution

Abstract

This study aimed to develop new closed-form and efficient estimators for the parameters of the bivariate Weibull distribution. New estimators can be produced using closed-form -consistent estimators for all parameters, except for the association parameter for which the estimator is not in closed form. This is carried out by utilizing a theorem that produces asymptotically efficient estimators. To achieve this, -consistent estimators are introduced. Fisher observed and expected information matrices are derived and used to develop new estimators. A simulation study and real data application are included to validate the new estimators. Given that the new estimators are as asymptotically efficient as maximum likelihood estimators and are in closed form, except for the association parameter, they can be used effectively in state-space modelling or real-time processing models. This is because of the shorter computing time associated with them than with maximum likelihood estimators.