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Empirical Laplace transform and approximation of compound distributions

Published online by Cambridge University Press:  14 July 2016

Sándor Csörgő  and
Jef L. Teugels
Sándor Csörgő*
Affiliation:
Szeged University
Jef L. Teugels*
Affiliation:
Katholieke Universiteit Leuven
*
∗Postal address: Bolyai Intezete, Szeged University, H-6720 Szeged, Aradi vértanúk tere 1, Hungary.
∗∗Postal address: Department of Mathematics, Katholieke Universiteit Leuven, Celestijnenlaan 200B, B-3030 Leuven, Belgium.
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Abstract

Let be i.i.d. non-negative random variables with d.f. F and Laplace transform L. Let N be integer valued and independent of In many applications one knows that for y → ∞ and a function φ where in turn τ is the solution of an equation On the basis of a sample of size n we derive an estimator τ n for τ by solving ψ (τ n, Ln(τ n), L′n(τ n), · ··) = 0 where Ln is the empirical version of L. This estimator is then used to derive the asymptotic behaviour of φ (y, τ n, Ln(τ n), L′n(τ n), · ··). We include five examples, some of which are taken from insurance mathematics.

Keywords

PROBABILITY OF RUININSURANCE MATHEMATICS
Type
Research Papers
Information
Journal of Applied Probability , Volume 27 , Issue 1 , March 1990 , pp. 88 - 101
Copyright
Copyright © Applied Probability Trust 1990 

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Footnotes

Work partially supported by the Hungarian National Foundation for Scientific Research, Grants 1808/86 and 457/88.

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