Article contents
A property of longtailed distributions
Published online by Cambridge University Press: 14 July 2016
Abstract
We investigate sufficient conditions so that is subexponential. Here F is a distribution function on [0, ∞[, with finite mean. Some applications to risk theory and rates of convergence in renewal theory are given.
- Type
- Research Papers
- Information
- Copyright
- Copyright © Applied Probability Trust 1984
References
Bingham, N. H. and Goldie, C. M. (1982) Extensions of regular variation, I: Uniformity and quantifiers. Proc. London Math. Soc.
44, 473–496.CrossRefGoogle Scholar
Chover, J., Ney, P. and Wainger, S. (1973) Functions of probability measures. J. Analyse Math.
26, 255–302.CrossRefGoogle Scholar
De Haan, L. and Resnick, S. I. (1982) Stochastic compactness and point processes. Report 8136/5, Econometric Institute, Erasmus University Rotterdam.Google Scholar
Embrechts, P. (1982) Subexponential distribution functions and their applications, A review. Proc. 7th Brasov Conf. Probability Theory.
Google Scholar
Embrechts, P. and Goldie, C. M. (1980) On closure and factorisation theorems for subexponential and related distributions. J. Austral. Math. Soc.
A 29, 243–256.CrossRefGoogle Scholar
Embrechts, P., Goldie, C. M. and Veraverbeke, N. (1979) Subexponentiality and infinite divisibility. Z. Wahrscheinlichkeitsth.
49, 335–347.CrossRefGoogle Scholar
Embrechts, P. and Omey, E. (1982) Functions of power series. Preprint, Leuven, K. U., Department of Mathematics.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
Frenk, J. B. G. (1983) The behaviour of the renewal sequence in case the tail of the waiting-time distribution is regularly varying with index – 1. Adv. Appl. Prob.
14, 870–884.Google Scholar
Goldie, C. M. (1978) Subexponential distributions and dominated-variation tails. J. Appl. Prob.
15, 440–442.Google Scholar
Grübel, R. (1982) Functions of discrete probability measures: Output approximation by linear combinations of input convolution powers. Z. Wahrscheinlichkeitsth.
64, 341–357.CrossRefGoogle Scholar
Ney, P. (1981) A refinement of the coupling method in renewal theory. Stoch. Proc. Appl.
11, 11–26.CrossRefGoogle Scholar
Pakes, A. G. (1975) On the tails of waiting-time distributions. J. Appl. Prob.
12, 555–564.Google Scholar
Pitman, E. J. G. (1980) Subexponential distribution function
J. Austral. Math. Soc.
A 29, 337–347.CrossRefGoogle Scholar
Seneta, E. (1976) Regularly Varying Functions. Lecture Notes in Mathematics 508, Springer-Verlag, Berlin.Google Scholar
Veraverbeke, N. (1977) Asymptotic behaviour of Wiener–Hopf factors of a random walk. Stoch. Proc. Appl.
5, 27–31.Google Scholar
- 43
- Cited by