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On simulation from infinitely divisible distributions

Published online by Cambridge University Press:  01 July 2016

Lennart Bondesson
Lennart Bondesson*
Affiliation:
University of Umeå
*
∗Postal address: Institute of Mathematical Statistics, University of Umeå, S-901 87 Umeå, Sweden.
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Abstract

A general method based on a limit theorem for generation of random numbers from infinitely divisible distributions with essentially given Lévy measure is studied. Some classes of infinitely divisible distributions that appear in a natural way in this context are paid particular attention.

Keywords

SHOT-NOISE DISTRIBUTIONSELF-DECOMPOSABILITYGENERALIZED GAMMA CONVOLUTIONSTABLE DISTRIBUTIONNORMAL APPROXIMATION
Type
Research Article
Information
Advances in Applied Probability , Volume 14 , Issue 4 , December 1982 , pp. 855 - 869
Copyright
Copyright © Applied Probability Trust 1982 

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References

Bartels, R. (1978) Generating non-normal stable variates using limit theorem properties. J. Statist. Compia. Simul. 7, 199–212.CrossRefGoogle Scholar
Berg, C. and Forst, G. (1982) A convolution equation relating the generalized G-convolutions and the Bondesson class. Scand. Acturial J. (1982).CrossRefGoogle Scholar
Bondesson, L. (1979) On generalized gamma and generalized negative binomial convolutions, Part I. Scand. Actuarial J. (1979), 125–146.CrossRefGoogle Scholar
Bondesson, L. (1981) Classes of infinitely divisible distributions and densities. Z. Wahrscheinlichkeitsth. 57, 39–71 (Correction and addendum note 59, 277).CrossRefGoogle Scholar
Chambers, J. M., Malllows, C. L. and Stuck, B. W. (1976) A method for simulating stable random variables. J. Amer. Statist. Assoc. 71, 340–344.CrossRefGoogle Scholar
Chung, K. L. (1974) A Course in Probability Theory, 2nd edn. Academic Press, New York.Google Scholar
Feller, W. (1971) An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edn. Wiley, New York.Google Scholar
Ferguson, T. (1973) A Bayesian analysis of some nonparametric problems. Ann. Statist. 1, 209–230.CrossRefGoogle Scholar
Kennedy, W. J. and Gentle, J. E. (1980) Statistical Computing. Dekker, New York.Google Scholar
Kent, J. (1982) The spectral decomposition of a diffusion hitting time. Ann. Prob. 10, 207–219.CrossRefGoogle Scholar
Lawrance, A. J. (1982) The innovation distribution of a gamma distributed autoregressive process. Scand. J. Statist. 9.Google Scholar
McKenzie, E. (1982) Product autoregression: a time-series characterization of the gamma distribution. J. Appl. Prob. 19, 463–468.CrossRefGoogle Scholar
Moran, P. A. P. (1968) An Introduction to Probability Theory. Clarendon Press, Oxford.Google Scholar
Thorin, O. (1977) On the infinite divisibility of the Pareto distribution. Scand. Actuarial J. (1977), 31–40.CrossRefGoogle Scholar
Thorin, O. (1978) An extension of the notion of a generalized G-convolution. Scand. Actuarial J. (1978), 141–149.CrossRefGoogle Scholar