A novel method for fitting unimodal continuous distributions on a bounded domain utilizing expert judgment estimates

Recent advances in computation technology for simulation/uncertainty analyses have shed new light on the triangular distribution and its use to describe the uncertainty of bounded input phenomena. Herein, we develop a novel fitting procedure for a continuous unimodal (four-parameter) family of distributions on a bounded domain, utilizing three properly selected quantile estimates and an estimate of the most likely value. The family in question is the two-sided power family of which the triangular distribution is a member. We analyze some of the procedure's fitting characteristics and use them to estimate the waiting time distribution in a stationary M/G/1 queuing system and the completion time distribution of a small project network example taken from the shipbuilding domain.