Estimating the Second-Order Parameter of Regular Variation and Bias Reduction in Tail Index Estimation Under Random Truncation

  • Nawel Haouas
  • Abdelhakim NecirEmail author
  • Brahim Brahimi
Original Article


In this paper, we proposed an estimator of the second-order parameter of randomly truncated Pareto-type distributions data and establish its consistency and asymptotic normality. Moreover, we derive an asymptotically unbiased estimator for the tail index and study its limit distribution. We show, by simulation, that the proposed estimators behave well, in terms of bias, root mean square error and standard error.


Bias reduction Extreme value index Product limit estimator Random truncation Second-order parameter 

Mathematics Subject Classification

60F17 62G30 62G32 62P05 



We are grateful to two referees for a careful reading of the manuscript and several useful comments.


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Copyright information

© Grace Scientific Publishing 2018

Authors and Affiliations

  • Nawel Haouas
    • 1
  • Abdelhakim Necir
    • 1
    Email author
  • Brahim Brahimi
    • 1
  1. 1.Laboratory of Applied MathematicsMohamed Khider UniversityBiskraAlgeria

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