Let , be independently distributed, where and are unknown. A Bayesian approach is used to estimate the first two moments of the minimum order statistic, . In order to compute the Bayes estimates, one has to evaluate the predictive densities of the conditional on past data. Although the required predictive densities are complicated in form, an efficient algorithm to calculate them has been developed and given in the article. An application of the Bayesian method in a continuous-review control model with multiple suppliers is discussed.
