A Bound for the Distribution of Smirnov’s Statistics

Let be the empirical distribution function for a sample of independent identically distributed random variables with distribution function . It is possible to prove the following inequality with some unspecified constant . There are some reasons based on numerous calculations to think that . It is s...

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Bibliographic Details
Published in:Lobachevskii journal of mathematics 2021-02, Vol.42 (2), p.351-367
Main Authors: Doynikov, A. N., Kruglov, V. M.
Format: Article
Language:English
Subjects:
Algebra
Analysis
Distribution functions
Geometry
Independent variables
Mathematical analysis
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Random variables
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Summary:Let be the empirical distribution function for a sample of independent identically distributed random variables with distribution function . It is possible to prove the following inequality with some unspecified constant . There are some reasons based on numerous calculations to think that . It is shown in this paper that this hypothesis is true for .
ISSN:1995-0802
1818-9962
DOI:10.1134/S1995080221020104