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Characterization of tails through hazard rate and convolution closure properties

Part of: Distribution theory - Probability Mathematical economics

Published online by Cambridge University Press:  14 July 2016

Anastasios G. Bardoutsos  and
Dimitrios G. Konstantinides
Anastasios G. Bardoutsos
Affiliation:
University of the Aegean, Department of Statistics and Actuarial - Financial Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, Greece. Email address: [email protected]
Dimitrios G. Konstantinides
Affiliation:
University of the Aegean, Department of Statistics and Actuarial - Financial Mathematics, University of the Aegean, Karlovassi, GR-83 200 Samos, Greece. Email address: [email protected]
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Abstract

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We use the properties of the Matuszewska indices to show asymptotic inequalities for hazard rates. We discuss the relation between membership in the classes of dominatedly or extended rapidly varying tail distributions and corresponding hazard rate conditions. Convolution closure is established for the class of distributions with extended rapidly varying tails.

Keywords

Subexponentialityextended rapidly varying taildominatedly varying tailMatuszewska indexhazard rate function

MSC classification

Primary: 60E05: Distributions
Secondary: 91B30: Risk theory, insurance
Type
Part 3. Heavy Tail Phenomena
Information
Journal of Applied Probability , Volume 48 , Issue A: New Frontiers in Applied Probability (Journal of Applied Probability Special Volume 48A) , August 2011 , pp. 123 - 132
Copyright
Copyright © Applied Probability Trust 2011 

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