Predictive distributions in risk analysis and estimation for the triangular distribution

Many Monte Carlo simulation studies have been done in the field of risk analysis. This article demonstrates the importance of using predictive distributions (the estimated distributions of the explanatory variable accounting for uncertainty in point estimation of parameters) in the simulations. We explore different types of predictive distributions for the normal distribution, the lognormal distribution and the triangular distribution. The triangular distribution poses particular problems, and we found that estimation using quantile least squares was preferable to maximum likelihood.