Exact propagation of uncertainties in multiplicative models

Propagation of uncertainties has been widely accepted as an integral component in health risk assessments. Historically, the approximations based on Taylor series expansions have been applied, but they are valid only when the model is linear or the coefficients of variation are small. Another approximation approach is Monte Carlo analysis. It is simpler and more practical for risk management but may become cumbersome if the model involves many variables containing large uncertainties. Recently, the exact log transform technique has been proposed for multiplicative models with lognormal uncertainties. The purpose of this paper is to present a novel exact analytical method as a complementary approach to simulation for general multiplicative models with independent variables, without a constraint on the types of uncertainty distributions. It also provides good estimates of the mean and variance of highly skewed distributions, determination of their existence, and verification of sufficient simulation sample size for simulation method. Two case examples are given to demonstrate the applications.