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Tytuł artykułu

On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution

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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)).
Twórcy
  • Technical University, 90-924 Łódź, A. Politechniki 11
Bibliografia
  • [1] F.J. Dyson, Fourier transforms of distributions functions, Canad J. Math. 5 (4) (1953), 554-558.
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  • [13] J. Marcinkiewicz and A. Zygmund, Quelques Theoremes sur les fonctions independantes, Studia Mathematica 7 (1938).
  • [14] D. Mieshalkin and B.A. Rogozin, An estimation of the distance betweenc.d.f.'s based on the knowledge of the absolute value of their corresponding characteristic functions and its application to the central limit theorem, The limit theorems of Probability Theory, Uzbek. Ac. Sci., Taskent 1963 (in Russian).
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  • [21] Tables of integral transforms, Vol. I, Mc Graw Hill, New York 1954.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1012
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