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On the estimation of the variability in the distribution tail

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 : Friday, October 23, 2020 - 10:03:41 AM
Last modification on : Tuesday, October 19, 2021 - 11:25:51 AM

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Laurent Gardes, Stéphane Girard. On the estimation of the variability in the distribution tail. Test, Spanish Society of Statistics and Operations Research/Springer, In press, ⟨10.1007/s11749-021-00754-2⟩. ⟨hal-02400320v2⟩

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