Sankhya: The Indian Journal of Statistics

1994, Volume 56, Series A, Pt. 3 , pp. 480-499

ON THE USE OF RECORD VALUES TO ESTIMATE THE LOCATION AND SCALE PARAMETERS OF THE GENERALIZED EXTREME VALUE DISTRIBUTION

By

MOHAMMAD AHSANULLAH, Rider College

and

BURT HOLLAND, Temple University

 

SUMMARY. The problem of estimating the location and scale parameters of the generalized extreme value distribution is studied under the assumption that the only available data are the record values. Minimum variance linear unbiased estimators (MVLUE), best linear invariant estimators (BLIE) and maximum likelihood estimators of these parameters are derived. Computer simulation is used to compare the properties of the MVLUE and BLIE. Several estimators of the shape parameter are also discussed. Predictors of the $s$-th record value based on the first $m\; (m < s)$ record values are derived and theoretically compared. The methodology is applied to an Olympic record data set.

AMS (1991) subject classification. 62E15; secondary 62F10.

Key words and phrases. Best linear invariant estimation, maximum likelihood estimation, minimum variance linear unbiased estimation, order statistics, prediction of records.

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