Fuzzy Reliability Estimation for Benktander Distribution

Naser Odat^1,*

¹Department of Mathematics, Jadara University, P.O. Box (733), postal code 21111, Irbid, Jordan

Email: nodat@jadara.edu.jo

Abstract

The fuzzy reliability estimate for the Benktander distribution, a model appropriate for heavy-tailed data, is investigated in this work. By adding membership functions and α-cuts, we extend the Benktander distribution to a fuzzy framework and compute its probability density function and reliability function. The fuzzy reliability is estimated using two methods: maximum likelihood and Bayesian approaches. The Bayesian method uses special loss functions, gamma priors, and squared error. The effectiveness of these estimators is examined in a simulated study using varying sample sizes and parameter values. The findings show that, especially for smaller samples, Bayesian techniques—in particular, the cautious Bayes estimator—perform better in terms of accuracy and stability than maximum likelihood estimation. The results emphasize how crucial it is to choose suitable prior distributions and loss functions while doing reliability analysis.

Keywords: Benktander Distribution; Fuzzy Reliability; Maximum likelihood; Bayesian estimator