Discussiones Mathematicae Probability and Statistics 20(2) (2000) 211-221

ON MIESHALKIN-ROGOZIN THEOREM AND SOME PROPERTIES OF THE SECOND KIND BETA DISTRIBUTION

Włodzimierz Krysicki

Technical University
90-924 Łódź, A. Politechniki 11

Abstract

The decomposition of the r.v. X with the beta second kind distribution in the form of finite (formula (9), Theorem 1) and infinity products (formula (17), Theorem 2 and form (21), Theorem 3) are presented. Next applying Mieshalkin - Rogozin theorem we receive the estimation of the difference of two c.d.f. F(x) and G(x) when sup|f(t) - g(t)| is known, improving the result of Gnedenko - Kolmogorov (formulae (23) and (24)).

Keywords: Mieshalkin - Rogozin theorem, result of Kolmogorov, Knar formula.

1999 Mathematics Subject Classiffication: 60E07, 62E15.

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Received 10 February 2000
Revised 10 August 2000