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Papers by Jef Teugels

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Abstract: In this paper we investigate and compare a number of real inversion formulas for the La... more Abstract: In this paper we investigate and compare a number of real inversion formulas for the Laplace transform. The focus is on the accuracy and applicability of the formulas for nu-merical inversion. In this contribution, we study the performance of the formulas for measures concentrated on a positive half-line to continue with measures on an arbitrary half-line.

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Lecture Notes in Economics and Mathematical Systems

ABSTRACT We make a first attempt to give an extreme value analysis of data, connected to catastro... more ABSTRACT We make a first attempt to give an extreme value analysis of data, connected to catastrophic events. While the data are readily accessible from SWISSRE, their analysis doesn’t seem to have been taken up. A first set refers to insured claims over the last 35 years; the second deals with victims from natural catastrophes. Together these sets should provide ample proof that extreme value analysis might be able to catch some essential information that traditional statistical analysis might overlook. We finish with a number of cautious remarks.

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Statistics of Extremes

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Statistics of Extremes

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Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random va... more Let \{X_1, X_2, ...\} be a sequence of independent and identically distributed positive random variables of Pareto-type with index \alpha>0 and let \{N(t); t\geq 0\} be a counting process independent of the X_i's. For any fixed t\geq 0, define T_{N(t)}:=\frac{X_1^2 + X_2^2 + ... + X_{N(t)}^2} {(X_1 + X_2 + ... + X_{N(t)})^2} if N(t)\geq 1 and T_{N(t)}:=0 otherwise. We derive limiting distributions for T_{N(t)} by assuming some convergence properties for the counting process. This is even achieved when both the numerator and the denominator defining T_{N(t)} exhibit an erratic behavior (\mathbb{E}X_1=\infty) or when only the numerator has an erratic behavior (\mathbb{E}X_1<\infty and \mathbb{E}X_1^2=\infty). Thanks to these results, we obtain asymptotic properties pertaining to both the sample coefficient of variation and the sample dispersion.

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Theory of Probability and Mathematical Statistics

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Etude du probleme du domaine d'attraction de l'estimateur de Hill introduit comme un esti... more Etude du probleme du domaine d'attraction de l'estimateur de Hill introduit comme un estimateur du maximum de vraisemblance pour la queue d'une distribution. Extension des conditions de normalite asymptotique

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