Short Communications

Refinements of classical probability estimates

N. V. Sokolov

St. Tikhon's Orthodox University, Moscow

Abstract: In this paper we obtain several refinements of the classical probability estimates of Kolmogorov, Prokhorov, and Chebyshev using a generalization of the Prokhorov multidimensional analogue of the Chebyshev inequality.

Keywords: Chebyshev inequality; Kolmogorov inequality; Prokhorov inequality; specified upper and lower probability estimates; function discontinuity; discreteness of a random variable; discrete probability.

MSC: 60

Received: 01.11.2012

DOI: 10.4213/tvp4514

 English version: Theory of Probability and its Applications, 2014, 58:2, 331–333

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