Estimation of P(Y<X) for lognormal distribution. Issue 6 (2nd November 2022)

• Record Type: Journal Article
• Authors: Tripathi, Yogesh Mani; Petropoulos, C.; Jha, Mayank Kumar
• Is Part Of: Quality technology & quantitative management. Volume 19:Issue 6(2022)
• Page Start: 749
• Page End: 765
• Publication Date: 2022-11-02
• Subjects: Bayes estimator -- highest posterior density interval -- lognormal -- maximum likelihood estimator -- stress–strength model; 62F10 -- 62F15 -- 62N02; Quality control -- Periodicals; Quality control -- Statistical methods -- Periodicals; Industrial management -- Periodicals; Industrial management; Management -- Research -- Methodology -- Periodicals; Qualitative research -- Periodicals; Management; Quality control; Quality control -- Statistical methods; Periodicals; 658.00721
• DOI: 10.1080/16843703.2022.2052585
• Languages: English
• ISSNs: 1684-3703

Abstract

ABSTRACT: The problem of estimating a stress-strength parameter is considered under the assumption that both stress and strength variables follow independent lognormal distributions. The maximum likelihood estimator of this parametric function is obtained and based on its asymptotic distribution, approximate intervals are constructed. Properties of a heuristic estimator are studied as well. Bootstrap intervals are also constructed. Bayes estimator is derived against proper and improper prior distributions. We further compute credible intervals of stress–strength parameter using importance sampling. The empirical Bayes procedure is also discussed. Proposed point and interval estimators are compared numerically using Monte Carlo simulations. Analysis of a real data set is presented for illustration purposes.