Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-16T19:25:47.386Z Has data issue: false hasContentIssue false
  • English
  • Français

Subexponential distributions and integrated tails

Published online by Cambridge University Press:  14 July 2016

Claudia Klüppelberg
Claudia Klüppelberg*
Affiliation:
Universität Mannheim
*
∗ Postal address: Seminar für Statistik, Universität Mannheim, D-6800 Mannheim, West Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

Let F be a distribution function on [0,∞) with finite expectation. In terms of the hazard rate of F several conditions are given which simultaneously imply subexponentiality of F and of its integrated tail distribution F1. These conditions apply to a wide class of longtailed distributions, and they can also be used in connection with certain random walks which occur in risk theory and queueing theory.

Keywords

INTEGRATED TAIL DISTRIBUTIONSUBEXPONENTIALITYDOMINATED VARIATIONRANDOM WALK THEORYRISK THEORYQUEUEING THEORY
Type
Research Papers
Information
Journal of Applied Probability , Volume 25 , Issue 1 , March 1988 , pp. 132 - 141
Copyright
Copyright © Applied Probability Trust 1988 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Beard, R. E., Pentikaeinen, T. and Pesonen, E. (1984) Risk Theory. Chapman and Hall, London.Google Scholar
Chover, J., Ney, P. and Wainger, S. (1973) Functions of probability measures. J. Analyse Math. 26, 255–302.Google Scholar
Embrechts, P. and Goldie, C. M. (1980) On closure and factorization properties of subexponential and related distributions. J. Austral. Math. Soc. A 29, 243–256.CrossRefGoogle Scholar
Embrechts, P. and Goldie, C. M. (1982) On convolution tails. Stoch. Proc. Appl. 13, 263–278.Google Scholar
Embrechts, P. and Omey, E. (1984) A property of longtailed distributions. J. Appl. Prob. 21, 80–87.Google Scholar
Embrechts, P. and Veraverbeke, N. (1982) Estimates for the probability of ruin with special emphasis on the possibility of large claims. Insurance Math. Econom. 1, 55–72.CrossRefGoogle Scholar
Goldie, C. M. (1978) Subexponential distributions and dominated-variation tails. J. Appl. Prob. 15, 440–442.CrossRefGoogle Scholar
Omey, E. and Willekens, E. (1984) Second-order behaviour of the tail of a subordinated probability distribution I. Katholieke Universiteit Leuven.Google Scholar
Pitman, E. J. G. (1980) Subexponential distribution functions. J. Austral. Math. Soc. A 29, 337–347.CrossRefGoogle Scholar
Pratt, J. W. (1960) On interchanging limits and integrals. Ann. Math. Statist. 31, 74–77.CrossRefGoogle Scholar
Teugels, J. L. (1975) The class of subexponential distributions. Ann. Prob. 3, 1000–1011.Google Scholar
Veraverbeke, N. (1977) Asymptotic behaviour of Wiener-Hopf factors of a random walk. Stoch. Proc. Appl. 5, 27–37.Google Scholar