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

Włodzimierz Krysicki

Discussiones Mathematicae Probability and Statistics (2000)

  • Volume: 20, Issue: 2, page 211-221
  • ISSN: 1509-9423

Abstract

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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)).

How to cite

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Włodzimierz Krysicki. "On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution." Discussiones Mathematicae Probability and Statistics 20.2 (2000): 211-221. <http://eudml.org/doc/287758>.

@article{WłodzimierzKrysicki2000,
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)).},
author = {Włodzimierz Krysicki},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {Mieshalkin - Rogozin theorem; result of Kolmogorov; Knar formula; Mieshalkin-Rogozin theorem},
language = {eng},
number = {2},
pages = {211-221},
title = {On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution},
url = {http://eudml.org/doc/287758},
volume = {20},
year = {2000},
}

TY - JOUR
AU - Włodzimierz Krysicki
TI - On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution
JO - Discussiones Mathematicae Probability and Statistics
PY - 2000
VL - 20
IS - 2
SP - 211
EP - 221
AB - 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)).
LA - eng
KW - Mieshalkin - Rogozin theorem; result of Kolmogorov; Knar formula; Mieshalkin-Rogozin theorem
UR - http://eudml.org/doc/287758
ER -

References

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