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March, 1953 A Modification of Schwarz's Inequality with Applications to Distributions
Sigeiti Moriguti
Ann. Math. Statist. 24(1): 107-113 (March, 1953). DOI: 10.1214/aoms/1177729088


Theorem 1 provides us with a result from which we can derive the modified Schwarz inequality (1.2) or, more generally, (3.8). The formulas hold when $x(t)$ is any nondecreasing function belonging to a certain wide class, and $\bar{\varphi}(t)$ is the right-hand derivative of the "greatest convex minorant" of $\Phi(t)$. The necessary and sufficient conditions for equality to hold are also given. Applications to distribution problems in statistics are discussed in Section 4.


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Sigeiti Moriguti. "A Modification of Schwarz's Inequality with Applications to Distributions." Ann. Math. Statist. 24 (1) 107 - 113, March, 1953.


Published: March, 1953
First available in Project Euclid: 28 April 2007

zbMATH: 0050.35301
MathSciNet: MR53166
Digital Object Identifier: 10.1214/aoms/1177729088

Rights: Copyright © 1953 Institute of Mathematical Statistics

Vol.24 • No. 1 • March, 1953
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