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EXTREME VALUE DISTRIBUTIONS FOR BIASED SAMPLES

Published online by Cambridge University Press:  20 January 2015

George Tzavelas  and
Polychronis Economou
George Tzavelas*
Affiliation:
Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou str., 185 34 Piraeus, Greece
Polychronis Economou
Affiliation:
Department of Civil Engineering, University of Patras, Rion-Patras, Greece E-mail: [email protected]
*
E-mail: [email protected] (Corresponding author)
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Abstract

In this work, the relationship between the extreme value distributions of the parent and its weighted counterpart distribution is studied. Sufficient conditions are provided in terms of the weight w(x) under which the weighted and parent distributions belong to the same attractor (Fréchet, Weibull, or Gumbel) and the relation of the corresponding shape parameters of the limiting distributions is presented. Additionally, a biased sampling corrected extreme value index is proposed, when the extreme value index is estimated from a biased sample. Finally, some simulation results are presented that suggest the superiority of a biased sample in estimating the extreme value index.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 2 , April 2015 , pp. 277 - 290
Copyright
Copyright © Cambridge University Press 2015 

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