Estimation of R for geometric distribution under lower record values

Abstract

In this paper, the estimation of the stress-strength model R=P(Y<X), based on lower record values is derived when both X and Y are independent and identical random variables with geometric distribution. Estimating R with maximum likelihood estimator and Bayes estimator with non-informative prior information based on mean square errors and LINIX loss functions for geometric distribution are obtained. The confidence intervals of R are constructed by using exact, bootstrap and Bayesian methods. Finally, different methods have been used for illustrative purpose by using simulation. The main results are obtained and introduced through a set of tables and figures with discussions.