Quantile-Parameterized Distributions for Expert Knowledge Elicitation

This paper provides a comprehensive overview of quantile-parameterized distributions (QPDs) as a tool for capturing expert predictions and parametric judgments. We survey a range of methods for constructing distributions that are parameterized by a set of quantile-probability pairs and describe an approach to generalizing them to enhance their tail flexibility. Furthermore, we explore the extension of QPDs to the multivariate setting, surveying the approaches to construct bivariate distributions, which can be adopted to obtain distributions with quantile-parameterized margins. Through this review and synthesis of the previously proposed methods, we aim to enhance the understanding and utilization of QPDs in various domains. Funding: U. Sahlin was funded by the Crafoord Foundation [ref 20200626]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/deca.2024.0219 .