| Tempered power laws arise in many applications like statistical physics, finance, hydrology, atmospheric science etc. These laws combine both heavy and light tails in the following fashion: in a short time frame they behave like a power law and in a long time frame they decay exponentially fast. In this talk, we suggest a method of estimating the tail parameter and extreme quantiles for these laws using a conditional likelihood approach in parallel to the Hill Estimator. We also discuss the asymptotic properties of this estimator and present some simulation results.
(This talk is based on an ongoing joint work with Mark M. Meerschaert and Qin Shao.) |