Johnson Quantile-Parameterized Distributions

In the field of decision analysis, it is common practice to elicit data points from continuous uncertainties from experts, and then fit a continuous probability distribution to the corresponding probability quantile pairs. This process often requires curve fitting and can result in a distribution that does not pass through any of the points provided by the expert.

In this paper [$], authors Christopher C. Hadlock and J. Eric Bickel develop a new family of continuous distributions that are parameterized by their quantiles. Their system is a strategic extension of the Johnson Distribution System, but can honor any symmetric percentile triplet of quantile assessments (e.g., the 10th-50th-90th) in conjunction with specified support bounds.

The authors’ new system is practical, flexible, and, as they demonstrate, able to match the shapes of numerous commonly named distributions.

This paper builds on the work of Thomas W. Keelin and Brad Powley of SDG, published in 2011 as “Quantile-Parmeterized Distributions.”

Published in 2017 in Decision Analysis. The abstract is free and the paper is available for purchase at this link..