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April, 1973 Bounds on Distribution Functions in Terms of Expectations of Order- Statistics
C. L. Mallows
Ann. Probab. 1(2): 297-303 (April, 1973). DOI: 10.1214/aop/1176996981

Abstract

Suppose $x_1, \cdots, x_n$ are the order-statistics of a random sample from a distribution $F$. We assume that the expectations $\xi_{i:n} = E(x_i)$ are known, and derive sharp bounds on $F(x)$ for all $x$. These results are obtained by transforming the problem into a classical one involving ordinary power moments.

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C. L. Mallows. "Bounds on Distribution Functions in Terms of Expectations of Order- Statistics." Ann. Probab. 1 (2) 297 - 303, April, 1973. https://doi.org/10.1214/aop/1176996981

Information

Published: April, 1973
First available in Project Euclid: 19 April 2007

zbMATH: 0261.62034
MathSciNet: MR356358
Digital Object Identifier: 10.1214/aop/1176996981

Subjects:
Primary: 62G30
Secondary: 26A87 , 60E05

Keywords: Chebyshev , distribution functions , Inequalities‎ , order statistics

Rights: Copyright © 1973 Institute of Mathematical Statistics

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Vol.1 • No. 2 • April, 1973
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