BAYESIAN CONFIDENCE-INTERVALS FOR THE PRODUCT OF 3 NORMAL MEANS

The problem of estimating the product of three normal means of three i ndependent normal distributions is considered. These types of estimati on problems arise in many environmental applications, such as exposure assessment and risk modeling. Classical confidence interval estimates are available in the literature; we consider the problem from the Bay esian approach using two different proper prior distributions and one non-informative prior distribution. Assuming the quadratic loss, Bayes ian estimates and Bayesian confidence intervals are given. Numerical i ntegration or simulation are necessary to evaluate such confidence int ervals. Computer programs written in Fortran are given to calculate th ese confidence intervals. Examples are provided.