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On the estimation of the variability in the distribution tail

Laurent Gardes 1 Stephane Girard 2
2 MISTIS [2016-2019] - Modelling and Inference of Complex and Structured Stochastic Systems [2016-2019]
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann , Grenoble INP [2007-2019] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2007-2019]
Abstract : We propose a new measure of variability in the tail of a distribution by applying a Box-Cox transformation of parameter $p ≥ 0$ to the tail-Gini functional. It is shown that the so-called Box-Cox Tail Gini Variability measure is a valid variability measure whose condition of existence may be as weak as necessary thanks to the tuning parameter p. The tail behaviour of the measure is investigated under a general extreme-value condition on the distribution tail. We then show how to estimate the Box-Cox Tail Gini Variability measure within the range of the data. These methods provide us with basic estimators that are then extrapolated using the extreme-value assumption to estimate the variability in the very far tails. The finite sample behavior of the estimators is illustrated both on simulated and real data.
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https://hal.inria.fr/hal-02400320
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Submitted on : Monday, December 9, 2019 - 2:29:29 PM
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Laurent Gardes, Stephane Girard. On the estimation of the variability in the distribution tail. 2019. ⟨hal-02400320⟩

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