Statistical models for exceedances with applications to finance and environmental statistics [Elektronische Ressource] / vorgelegt von Ulf Cormann

Ulr Cormann

Description

Statistical Models forExceedances with Applications toFinance and EnvironmentalStatisticsDissertationzur Erlangung des Grades eines Doktorsder Naturwissenschaftenvorgelegt vonM.Sc. Ulf Cormanngeb. am 25.01.1982 in Mendeneingereicht beim Fachbereich Mathematikder Universität SiegenSiegen 2009TAG DER MÜNDLICHEN PRÜFUNG:28.04.2010BETREUER UND GUTACHTER:Prof. Dr. Reiss, Universität SiegenProf. Dr. Scheffler, Universität SiegeniiiivAbstractThis thesis concerns statistical analysis for upper tails of distribution functions.Firstly, we derive asymptotic distributions of exceedances under general monotonetransformations and analyze the pertaining domains of attraction. It turns out thatall possible limiting distributions satisfy a certain form of a generalized pot–stability.We give a complete characterization of all strictly increasing, continuous limiting dis-tributions. Further, we deduce the class of all limiting distributions under power–normalization and characterize the pertaining domains of attraction. The limiting dis-tributions are identified as generalized log–Pareto and negative generalized log–Paretodistributions as well as a certain class of discrete distributions. Moreover, we intro-duceandstudyanextendedclassofgeneralizedlog–Paretodistributionsandprovideahybrid Maximum–Likelihood estimator. These distributions can serve as a parametricasymptotic model for super–heavy tailed distributions.

Sujets

• Mathematics

Informations

• Publié par: universitat_siegen
• Publié le: 01 janvier 2010
• Nombre de lectures: 20
• Langue: English
• Poids de l'ouvrage: 1 Mo

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