Empirically Evaluating the Flexibility of the Johnson Family of Distributions: A Crop Insurance Application

Abstract

This article examines the flexibility of the Johnson system of distributions by assessing its performance in terms of modeling crop yields for the purpose of setting actuarially fair crop insurance premiums. Using data from corn farms in Illinois coupled with Monte Carlo simulation procedures, we found that average crop insurance premiums computed on the basis of the Johnson system provide reasonably accurate estimates even when the data are normal or come from a non-normal distribution other than the Johnson system (i.e., a beta). These results suggest that there is potential for using the Johnson system to rate previously uninsured crops that do not have historical insurance performance data upon which to base premium calculations.