The Generalized Johnson Quantile-Parameterized Distribution System

Johnson quantile-parameterized distributions (J-QPDs) are parameterized by any symmetric percentile triplet (SPT) (e.g., the 10th–50th–90th) and support bounds. J-QPDs are smooth, highly flexible, and amenable to Monte Carlo simulation via inverse transform sampling. However, semibounded J-QPDs are limited to lognormal tails. In this paper we generalize the kernel distribution of J-QPD beyond the standard normal, generating new fat-tailed distribution systems that are more flexible than J-QPD. We also show how to augment the SPT/bound parameters with a tail parameter, lending separate control over the distribution body and tail. We then present advantages of our new generalized system over existing systems in the contexts of both expert elicitation and fitting to empirical data.