Displaying similar documents to “On a probability inequality for multivariate normal distribution”

Simple random walk and rank order statistics

Igor Očka (1977)

Aplikace matematiky

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The distributions of rank order statistics are studied for the case of arbitrary sample sizes in the two sample problem. The method applied is a generalization of Dwass's method from his paper in Ann. Math. Statist. 38 (1967), based on the analogy of rank order statistics and functions on a simple random walk.

The Lukacs-Olkin-Rubin theorem without invariance of the "quotient"

Konstancja Bobecka, Jacek Wesołowski (2002)

Studia Mathematica

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The Lukacs theorem is one of the most brilliant results in the area of characterizations of probability distributions. First, because it gives a deep insight into the nature of independence properties of the gamma distribution; second, because it uses beautiful and non-trivial mathematics. Originally it was proved for probability distributions concentrated on (0,∞). In 1962 Olkin and Rubin extended it to matrix variate distributions. Since that time it has been believed that the fundamental...

Evaluating improvements of records

Tomasz Rychlik (1997)

Applicationes Mathematicae

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We evaluate the extreme differences between the consecutive expected record values appearing in an arbitrary i.i.d. sample in the standard deviation units. We also discuss the relevant estimates for parent distributions coming from restricted families and other scale units.