Johnson Quantile-Parameterized Distributions

It is common decision analysis practice to elicit quantiles of continuous uncertainties and then fit a continuous probability distribution to the corresponding probability-quantile pairs. This process often requires curve fitting and the best-fit distribution will often not honor the assessed points. By strategically extending the Johnson Distribution System, we develop a new distribution system that honors any symmetric percentile triplet of quantile assessments (e.g., the 10th-50th-90th) in conjunction with specified support bounds. Further, our new system is directly parameterized by the assessed quantiles and support bounds, eliminating the need to apply a fitting procedure. Our new system is practical, flexible, and, as we demonstrate, able to match the shapes of numerous commonly named distributions.