Assessing the Extremes of Probability Distributions by the Fractile Method*

When people are asked to express uncertainty in the form of probability distributions (by assessing several fractiles of the cumulative distributions), experiments have shown that most subjects exhibit systematic biases in describing the extremes or tails of the distributions. This paper discusses methods designed to refine the assessments of such extremes of probability distributions. The techniques were tested on large samples of assessors; the effectiveness of different methods is reported. The methods include asking for the assessment of additional fractiles in the extremes, asking for different fractiles in the extremes (.10 and .90 instead of .01 and .99 fractiles), making the assessment a two‐step process by separating the questions about central fractiles from those requesting extreme values, and varying the order in which different fractile values are requested. All these methods except the two‐step process resulted in improved estimation of the extreme values of the distributions when compared to some of the early work in this field where five fractile assessments were made.