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
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.
Full paper (PDF)
This article in Mathematical Reviews