Using Tocher's curve to convert subjective quantile-estimates into a probability distribution function

Abstract

One standard approach for estimating a subjective distribution is to elicit subjective quantiles from a human expert. However, most decision-making models require a random variable's moments and/or distribution function instead of its quantiles. In the literature little attention has been given to the problem of converting a given set of subjective quantiles into moments and/or a distribution function. We show that this conversion problem is far from trivial, and that the most commonly used conversion procedure often produces large errors. An alternative procedure using `Tocher's curve' is proposed, and its performance is evaluated with a wide variety of test distributions. The method is shown to be more accurate than a commonly used procedure.