Estimating Probable Maximum Loss with Order Statistics

In the past there has been much discussion about the definition of probable maximum loss (PML), but little attention has been given to its quantification. This paper introduces the concept of order statistics as a tool to use in estimating the PML. Two different approaches, that of X(n), the largest sample value, and that of quantiles, lead to six specific methods to estimate the PML. Three of the methods require sample data, two of the methods require assumptions about the underlying distribution of the population and the frequency, and one of the methods requires only estimates of the mean and variance of the population and of the frequency. All six methods are illustrated using a particular size of loss distribution. The methods work equally as well if the distribution of size of loss as a percentage of value is available.