Open Access
November 2012 Bias-reduced estimation of Wang's two-sided deviation risk measure under Lévy-stable regime
Brahim Brahimi, Djamel Meraghni, Abdelhakim Necir, Sonia Touba
Afr. Stat. 7(1): 441-458 (November 2012).


Several risk measures, such as the distorted insurance premium and the two-sided deviation (TSD) measure, can be regarded as L-functionals with specific weight functions. In this paper, we focus on the TSD risk measure as we define a new estimator by using the bias-reduced estimators of extreme quantiles proposed by Li et al. 2010. A simulation study is carried out to compare, in terms of bias and mean squared error, the new estimator with that introduced recently by Necir and Meraghni 2010.


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Brahim Brahimi. Djamel Meraghni. Abdelhakim Necir. Sonia Touba. "Bias-reduced estimation of Wang's two-sided deviation risk measure under Lévy-stable regime." Afr. Stat. 7 (1) 441 - 458, November 2012.


Published: November 2012
First available in Project Euclid: 1 February 2013

zbMATH: 1258.91096
MathSciNet: MR3034389

Primary: 62G32 , 91B30
Secondary: 62G05 , 62G30

Keywords: bias reduction , high quantiles , Hill estimator , Lévy-stable distributions , L-statistics , order statistics , risk measure , second order regular variation , tail index

Rights: Copyright © 2012 The Statistics and Probability African Society

Vol.7 • No. 1 • November 2012
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