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.