Afrika Statistika

Robust estimator of distortion risk premiums for heavy-tailed losses

Brahim BRAHIMI and Kenioua ZOUBIR

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We use the so-called t-Hill tail index estimator proposed by Fabián (2001), rather than Hill's one, to derive a robust estimator for the distortion risk premium of losses. Under the second-order condition of regular variation, we establish its asymptotic normality. By simulation study, we show that this new estimator is more robust than of Necir and Meraghni (2009) both for small and large samples.


Nous utilisons l'estimateur de l'indice de queue dit t-Hill proposé par Fabián (2001), au lieu de l'estimateur de Hill, pour obtenir un estimateur robuste pour la prime de risque de distorsion des pertes. Sous la condition de second ordre de variation régulière, nous établissons sa normalité asymptotique. Par l'étude de simulation, nous montrons que ce nouvel estimateur est plus robuste que de celui proposé par Necir and Meraghni (2009) pour les petites et les grandes tailles d'échantillon.

Article information

Afr. Stat., Volume 11, Number 1 (2016), 869-882.

First available in Project Euclid: 22 April 2016

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G10: Hypothesis testing 62G32: Statistics of extreme values; tail inference

Distortion risk premiums Extreme values Tail Robustness


BRAHIMI, Brahim; ZOUBIR, Kenioua. Robust estimator of distortion risk premiums for heavy-tailed losses. Afr. Stat. 11 (2016), no. 1, 869--882. doi:10.16929/as/2016.869.80.

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