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

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.