Volume 2,  Issue 1, 2001

Article 6

SHARP BOUNDS ON QUASICONVEX MOMENTS OF GENERALISED ORDER STATISTICS

L. GAJEK AND A. OKOLEWSKI

INSTITUTE OF MATHEMATICS 
TECHNICAL UNIVERSITY OF LODZ
UL. ZWIRKI 36, 90-924 LODZ
POLAND
E-Mail: gal@ck-sg.p.lodz.pl

Received 11 June, 2000; accepted 11 October 2000.
Communicated by: S.S. Dragomir

ABSTRACT. Sharp lower and upper bounds for quasiconvex moments of generalized order statistics are proven by the use of rearranged Moriguti's inequality. Even in the second moment case, the method yields improvements of known quantile and moment bounds for the expectation of order and record statistics based on independent identically distributed random variables. The bounds are attainable providing new characterizations of three-point and two-point distributions.
Key words:
Generalized Order Statistics, Quasiconvex Moments, Moriguti Inequality, Steffensen Inequality.

2000 Mathematics Subject Classification:
62G30, 62H10.

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Some Aspects of Convex Functions and Their Applications
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Further Reverse Results for Jensen's Discrete Inequality and Applications in Information Theory
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Sharp Bounds on Quasiconvex Moments of Generalized Order Statistics 
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