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

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Cybernetics and Systems Analysis Aims and scope

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

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References

  1. W. J. Stadden and S. Karlin, Tchebycheff Systems: With Applications in Analysis and Statistics (Pure and Applied Mathematics, Vol. XV) (1966).

  2. H. P. Mulholland and C. A. Rogers, “Representation theorems for distribution functions,” in: Proc. London Math. Soc., Vol. 8, No. 3, 177–223 (1958).

  3. N. L. Johnson and C. A. Rogers, “The moment problem for unimodal distribution,” Ann. Math. Stat., Vol. 22, 433–439 (1951).

  4. L. Kleinrock, Queueing Theory, Wiley Interscience, Vol. 1 (1975), Vol. 2 (1976).

  5. M. G. Krein and A. A. Nudelman, The Markov Moment Problem and Extremal Problems, Translations of Mathematical Monographs, Vol. 50, American Mathematical Society (1977).

  6. L. S. Stoikova, “Necessary and sufficient condition of extremum for the Lebesgue–Stieltjes integral on a class of distributions,” Cybern. Syst. Analysis, Vol. 26, No. 1, 90–95 (1990).

  7. L. S. Stoikova, “Generalized Chebyshev inequalities and their application in the mathematical theory of reliability,” Cybern. Syst. Analysis, Vol. 46, No. 3, 472–476 (2010).

  8. L. S. Stoikova, “Greatest lower bound of system failure probability on a special time interval under incomplete information about the distribution function of the time to failure of the system,” Cybern. Syst. Analysis, Vol. 53, No. 2, 217–224 (2017).

  9. E. S. Ventsel and L. A. Ovcharov, Probability Theory [in Russian], Nauka, Moscow (1973).

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Authors and Affiliations

  1. V. M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    L. S. Stoikova

  2. Institute of Physics and Technology of National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine

    L. V. Kovalchuk

Authors
  1. L. S. Stoikova
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  2. L. V. Kovalchuk
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Correspondence to L. S. Stoikova.

Additional information

Translated from Kibernetika i Sistemnyi Analiz, No. 6, November–December, 2019, pp. 41–53.

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Stoikova, L.S., Kovalchuk, L.V. Exact Estimates for Some Linear Functionals of Unimodal Distribution Functions Under Incomplete Information. Cybern Syst Anal 55, 914–925 (2019). https://doi.org/10.1007/s10559-019-00201-z

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  • DOI: https://doi.org/10.1007/s10559-019-00201-z

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