On a Basis for 'Peaks Over Threshold' Modeling
Abstract
Peaks over Threshold models commonly used e.g. in hydrology, assume that peak values of an iid or stationary sequence X sub i above a high value u, occur at Poisson points, and the excess values of the peak above u are independent with an arbitrary common d.f. G. Motivation for these models has been provided by Smith by using Pareto-type approximations of Pickands for distributions of such excess values. These works strongly suggest that the Pareto family provides the appropriate class of distributions G for the POT model. This paper considers the point process of excess values of peaks above a high level u and demonstrate that this converges in distribution to a Compound Poisson Process as u approaches limit of infinity under appropriate assumptions. It is shown that the multiplicity distribution of this limit (i.e. the limiting distribution of excess values of peaks) must belong to the Pareto family and detailed forms are given for the normalizing constants involved. This exhibits the POT model specifically as a limit for the point process of excesses of peaks and delineates the distributions involved.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1990
- Accession Number
- ADA222571
Entities
People
- M. Ross Leadbetter
Organizations
- University of North Carolina at Chapel Hill