One of my dissertation chapters, “The QFlex Distribution”, coauthored with my advisors Eric Bickel and Ben Leibowicz, was recently published in Decision Analysis!

Quantile-parameterized distributions (QPDs) allow us to produce continuous probability distributions that directly match a handful of quantile assessments, such as an expert’s 10th, 50th, and 90th percentiles about an unknown quantity. QPDs’ ability to go from sparse expert estimates to a plausible probability distribution makes them a natural tool for decision analysis. In the paper, we introduce QFlex, a new QPD built entirely from monotone transformations of valid quantile functions. Unlike the widely used Metalog distribution, QFlex guarantees a valid distribution through simple coefficient constraints, so fits never need numerical repair afterwards. This guarantee doesn’t come at the cost of accuracy: across roughly 3,500 benchmark distributions from the Pearson system1, QFlex generally matches or exceeds the Metalog’s accuracy at moderate orders.

For further reading, a free preprint of the paper is available on SSRN.

  1. The Pearson system is a family of continuous distributions that spans a wide range of shapes, including the normal, beta, gamma, and Student’s t. It contains a distribution for every feasible combination of skewness and kurtosis, which makes it a natural benchmark for testing how flexible a distribution is. ↩