 On a basis for 'Peaks over Threshold' modelingM. R. Leadbetter Statistics & Probability Letters, 1991, vol. 12, issue 4, 357-362 Abstract: 'Peaks over Thresholds' ('POT') models commonly used e.g. in hydrology, assume that peak values of an i.i.d. or stationary sequence Xi 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 (1985, 1987), by using Pareto-type approximations of Pickands (1975) 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. In the present paper we consider 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-->[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. Date: 1991 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:stapro:v:12:y:1991:i:4:p:357-362 Ordering information: This journal article can be ordered from Access Statistics for this article Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul More articles in Statistics & Probability Letters from Elsevier |
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