The Bayesian estimation of reciprocal hazard rates in exponential populations under an unknown common shift in fuzzy environment

A random sample of size n is drawn independently from two shifted exponential populations. The reciprocal hazard rates and the common shift parameter are assumed to be unknown and represented as fuzzy quantities. Fuzzy Bayesian estimators of the reciprocal hazard rates are derived using suitable prior information. The squared-error loss function is employed for estimation. Limit Bayes estimators are also derived. The fuzzy estimators are first obtained using the α -cut technique and are subsequently defuzzified using a midpoint approximation to the centroid method to obtain crisp estimates. A simulation study is conducted for various sample sizes and parameter pairs ( λ 1 , λ 2 ) . The squared-error risks associated with the crisp and fuzzy estimators are estimated using Monte Carlo simulation. The simulation results illustrate the behavior of the estimators and their associated risks under different parameter settings and sample sizes.