Estimation of the stress–strength Reliability for Benktander Distribution

Naser Odat^1,*

¹Department of Mathematics, Faculty of Science, Jadara University, Irbid, Jordan

Email: nodat@jadara.edu.jo

Abstract

This work focuses on the estimation reliability function    where x and y are two independent Benktander distributions. The greatest likelihood's asymptotic distribution is found. The maximum likelihood estimator, the moment method estimator, and the approximate maximum likelihood estimator of are proposed. We obtain the asymptotic distribution of s maximum likelihood estimate. The  confidence interval can be found using the asymptotic distribution.

Keywords: Benktander; Maximum likelihood; Asymptotic distribution; Fisher information matrix