Cybernetics and Systems Analysis

, Volume 55, Issue 6, pp 914–925 | Cite as

Exact Estimates for Some Linear Functionals of Unimodal Distribution Functions Under Incomplete Information

  • L. S. StoikovaEmail author
  • L. V. Kovalchuk

Exact estimates are found for the probability that a non-negative unimodal random variable μ hits the interval (m − σμ, m + σμ) when mode m coincides with the fixed first moment of a random variable μ and \( {\sigma}_{\mu}^2 \) is a fixed variance of random variable μ. Also, a brief important auxiliary information is given with examples, statements, and author’s notations, which simplify obtaining the main result. The results of this study may be useful in evaluating the probability of hitting the projectile zone when aimed shooting


linear functionals of unimodal distribution functions and their extremum values Johnson–Rogers transformation exact generalized Chebyshev inequalities for unimodal distribution functions 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.V. M. Glushkov Institute of CyberneticsNational Academy of Sciences of UkraineKyivUkraine
  2. 2.Institute of Physics and Technology of National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic InstituteKyivUkraine

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