Geodesic
On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution
Discussiones Mathematicae. Probability and Statistics, Tome 20 (2000) no. 2, pp. 211-221

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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 
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Krysicki, Włodzimierz. On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution. Discussiones Mathematicae. Probability and Statistics, Tome 20 (2000) no. 2, pp. 211-221. http://geodesic.mathdoc.fr/item/DMPS_2000_20_2_a3/