An Experimental Comparison of Four Methods for Assessing Judgmental Distributions

For a number of statistical applications, experts' subjective estimates are needed for distributional parameters, like mean and variance; sometimes even the whole density is wanted. The literature agrees that it is wise behaviour to ask the expert only quantile estimates; from these, the desired parameter or density is derived. Many methods, using different sets of quantiles, have been suggested. A new method is proposed here. Experts are asked the relatively simple task of estimating the seven values that divide the total probability mass into eight equal parts. These seven quantiles uniquely determine one distribution within both the Pearson and the Johnson system of distributions. Comparisons between different methods were, in the past, generally based on theoretical arguments. A more practice-oriented approach is followed here: together with three often-used methods, our new method is tested experimentally: 56 students with some expert knowledge estimated quantiles of four distributions. The accuracy of the four methods in estimating both the quantiles and the distributional parameters is calculated and discussed