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ESTIMATION OF QUANTILES FOR A FRÉCHET‐TYPE DISTRIBUTION
Author(s) -
Hasofer A.M.,
Wang J.Z.
Publication year - 1996
Publication title -
australian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 0004-9581
DOI - 10.1111/j.1467-842x.1996.tb00683.x
Subject(s) - quantile , mathematics , estimator , order statistic , statistics , distribution (mathematics) , maximum likelihood , range (aeronautics) , type (biology) , stable distribution , domain (mathematical analysis) , econometrics , mathematical analysis , ecology , materials science , composite material , biology
Summary Estimation of high quantiles of a distribution in the domain of attraction of the Fréchet distribution is based on the extremal distribution of the k largest order statistics. The problem is treated by a local maximum likelihood method on a three parameter model. The estimators are shown to be asymptotically consistent for the whole range of the tail index parameter.