Estimation of P(Y<X) for lognormal distribution. Issue 6 (2nd November 2022) - Tripathi, Yogesh Mani; Petropoulos, C.; Jha, Mayank Kumar
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.