An inequality for order statistics

✍ Scribed by Anda Gadidov

• Book ID: 104302536
• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 134 KB
• Volume: 34
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(96)00158-7

✦ Synopsis

Let k be a non-negative integer, and let r~, r2 ..... rk be non-negative real numbers satisfying rl + r2 + ... + rk ~< 1 and ri+~ + ... + rk < (k -i)/k for all i = 1 ..... k -1. It is proved that there exists a constant c such that for any X~,X2 ..... Xk non-negative i.i.d, random variables, if X(y) denotes the jth order statistic, then the following inequality r I holds: EX(~)... X~)<~ cEX(~). Moreover, it is shown that the conditions on r l,..., rk are best possible for the inequality to hold.