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)).
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1012,
author = {W\l odzimierz Krysicki},
title = {On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution},
journal = {Discussiones Mathematicae Probability and Statistics},
volume = {20},
year = {2000},
pages = {211-221},
zbl = {0976.60028},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1012}
}
Włodzimierz Krysicki. On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution. Discussiones Mathematicae Probability and Statistics, Tome 20 (2000) pp. 211-221. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1012/
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