Grouping Loss Distributions by Tail Behavior Part III: Ordering Distributions

This three part paper addresses the task of modeling the right hand tail of a severity distribution. In Part I the excess ratio function is used to define a discrete sequence of loss distributions with related moments and similar tail behavior. Part II extends this to continuous one-parameter families and provides some examples. Part III provides the main result: that under some reasonable conditions, each such family has a limiting distribution which is exponential. The paper then exploits this to 1) group loss distributions based on tail behavior and 2) promote the choice of (mixed) exponentials to model tail behavior.