Inferences for stress–strength reliability of Burr Type X distributions based on ranked set sampling
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CitationAkgül, F. G., & Şenoğlu, B. (2020). Inferences for stress–strength reliability of Burr Type X distributions based on ranked set sampling. Communications in Statistics-Simulation and Computation.
In this study, we consider the point and interval estimation of the stress–strength reliability R = P(X < Y) based on ranked set sampling when the stress X and the strength Y are both independent Burr Type X random variables. In the context of point estimation, we obtain the maximum likelihood (ML) estimator of R using iterative methods. We also use Mehrotra and Nanda’s modified maximum likelihood methodology, which gives explicit estimator of R as an alternative to the ML methodology. In view of interval estimation, we construct the asymptotic confidence interval of R In addition, the bootstrap confidence intervals of R are constructed based on two different resampling methods. The performance of the proposed estimators (both point and interval) is compared with their simple random sampling counterparts. A real data set from an agricultural experiment is analyzed to show the implementation of the proposed methodologies.