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

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)).