The Generalized Johnson Quantile-Parameterized Distribution System

Christopher C. Hadlock () and J. Eric Bickel ()
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Christopher C. Hadlock: Operations Research and Industrial Engineering, The University of Texas at Austin, Texas 78712
J. Eric Bickel: Operations Research and Industrial Engineering, The University of Texas at Austin, Austin, Texas 78712

Decision Analysis, 2019, vol. 16, issue 1, 67-85

Abstract: 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.

Keywords: uncertainty; subjective probability; modeling; decision analysis; quantile function; power-law; power-law probability distribution; fat-tailed distribution; heavy-tailed distribution; quantile-probability data; practice (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:inm:ordeca:v:16:y:2019:i:1:p:67-85

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