Predictive densities for the lognormal distribution and their applications

Abstract

Maximum likelihood predictive densities (MLPDs) for a future lognormal observation are obtained and their applications to reliability and life testing are considered. When applied to reliability and failure rate estimations, they give estimators that can be much less biased and less variable than the usual maximum likelihood estimations (MLEs) obtained by replacing the unknown parameters in the density function by their MLEs. When applied to lifetime predictions, they give prediction intervals that are shorter than the usual frequentist intervals. Using the MLPDs, it is also rather convenient to construct the shortest prediction intervals. Extensive simulations are performed for comparisons. A numerical example is given for illustration. © 2000 Elsevier Science Ltd. All rights reserved.