Sequence of expectations of maximum-order statistics

✍ Scribed by J.S. Huang

• Book ID: 104302754
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 276 KB
• Volume: 38
• Category: Article
• ISSN: 0167-7152
• DOI: 10.1016/s0167-7152(97)00161-2

✦ Synopsis

Necessary and sufficient conditions for a given sequence of numbers {#,} to be the expectations of maximum order statistics are usually rather complicated -involving sequences of determinants. We obtain a very simple and intuitive sufficient condition: {#,} is monotonely increasing and for each k, the induced sequence of expectations of the kth largest-order statistics is also monotonely increasing. The condition is obviously necessary. It also leads to a simple bound for the expectation of order statistics, which is surprisingly sharp despite its simplicity. (~) 1998 Elsevier Science B.V.