Sankhya: The Indian Journal of Statistics

1999, Volume 61, Series A, Pt. 2, 229-240

UPPER BOUND FOR THE COVARIANCE OF EXTREME ORDER STATISTICS FROM A SAMPLE OF SIZE THREE

By

NICKOS PAPADATOS, University of Cyprus, Nicosia

SUMMARY. Papathanasiou (1990, Statist. Probab. Lett. 9 145--147) proved that the covariance of the ordered pair from a random sample of size two does not exceed the one third of the population variance. In the present note, by using Legendre polynomials, it is proved that a similar result holds for minimum and maximum from a sample of size three, and the equality characterizes the hyperbolic sine density.

AMS (1991) subject classification. Primary 60E15; secondary 62E10.

Key words and phrases. Characterization, order statistics, Legendre polynomials, covariance bounds, hyperbolic sine density.

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