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A NOTE ON THE CLOSURE OF CONVOLUTION POWER MIXTURES (RANDOM SUMS) OF EXPONENTIAL DISTRIBUTIONS

Part of: Limit theorems Distribution theory Distribution theory - Probability

Published online by Cambridge University Press:  01 February 2008

J. M. P. ALBIN
J. M. P. ALBIN*
Affiliation:
Department of Mathematics, Chalmers University of Technology, 412 96 Gothenburg, Sweden (email: palbin@math.chalmers.se)
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Abstract

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We make a correction to an important result by Cline [D. B. H. Cline, ‘Convolutions of distributions with exponential tails’, J. Austral. Math. Soc. (Series A)43 (1987), 347–365; D. B. H. Cline, ‘Convolutions of distributions with exponential tails: corrigendum’, J. Austral. Math. Soc. (Series A)48 (1990), 152–153] on the closure of the exponential class under convolution power mixtures (random summation).

Keywords

compound Poisson distributionconvolution powerexponential distributionrandom sumTauberian theorem

MSC classification

Secondary: 60F99: None of the above, but in this section 62E20: Asymptotic distribution theory 60E07: Infinitely divisible distributions; stable distributions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 84 , Issue 1 , February 2008 , pp. 1 - 7
Copyright
Copyright © 2008 Australian Mathematical Society

References

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