Identifying Tail Behavior by Means of Residual Quantile Functions

Abstract

Residual quantile functions characterize several important types of tail behavior. Graphical methods for identifying tail behavior starting from random samples are suggested. Graphics are used for exploring the existence of moments, the existence of the moment generating function, and regular and rapid variation tails. Simulations show the graphics perform well, even with relatively small samples. Our approach is illustrated with annual peak floods from a station in central Appalachia, and dentistry costs from a Colombian health service.

Key Words:

• Classes L _γ
• Existence of moments
• Existence of the moment generating function
• Hill statistic
• Rapid variation
• Regular variation