Models with hidden regular variation: Generation and detection

Abstract

We review the notions of multivariate regular variation (MRV) and hidden regular variation (HRV) for distributions of random vectors and then discuss methods for generating models exhibiting both properties concentrating on the non-negative orthant in dimension two. Furthermore we suggest diagnostic techniques that detect these properties in multivariate data and indicate when models exhibiting both MRV and HRV are plausible fits for the data. We illustrate our techniques on simulated data, as well as two real Internet data sets.

Keywords

• Regular variation
• multivariate heavy tails
• hidden regular variation
• tail estimation
• conditional extreme value model