Bayesian confidence intervals for the product of three normal means

Abstract

The problem of estimating the product of three normal means of three independent normal distributions is considered. These types of estimation 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 Bayesian approach using two different proper prior distributions and one non-informative prior distribution. Assuming the quadratic loss, Bayesian estimates and Bayesian confidence intervals are given. Numerical integration or simulation are necessary to evaluate such confidence intervals. Computer programs written in Fortran are given to calculate these confidence intervals. Examples are provided.