Bayesian statistics often requires eliciting prior probabilities from subject matter experts who are unfamiliar with statistics. While most people an intuitive understanding of the mean of a probability distribution, fewer people understand variance as well, particularly in the context of asymmetric distributions. Prior beliefs may be more accurately captured by asking experts for quantiles rather than for means and variances.
This note will explain how to solve for parameters so that common distributions satisfy two quantile conditions. We present algorithms for computing these parameters and point to corresponding software.
The distributions discussed are normal, log normal, Cauchy, Weibull,gamma, and inverse gamma. The method given for the normal and
Cauchy distributions applies more generally to any location-scale family.
Statistical Methodology | Statistical Models | Statistical Theory
Cook, John D., "Determining distribution parameters from quantiles" (January 2010). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 55.