# On the estimation of the variability in the distribution tail

2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann, INPG - Institut National Polytechnique de Grenoble
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.
Keywords :
Domain :
Complete list of metadatas

Cited literature [31 references]

https://hal.inria.fr/hal-02400320
Contributor : Stephane Girard <>
Submitted on : Monday, December 9, 2019 - 2:29:29 PM
Last modification on : Thursday, March 26, 2020 - 8:49:33 PM
Document(s) archivé(s) le : Tuesday, March 10, 2020 - 5:32:41 PM

### File

gini_allDA6.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-02400320, version 1

### Citation

Laurent Gardes, Stephane Girard. On the estimation of the variability in the distribution tail. 2019. ⟨hal-02400320⟩

Record views