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The multiple Cantelli inequalities

Author

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  • Haruhiko Ogasawara

    (Otaru University of Commerce)

Abstract

The Cantelli inequality or the one-sided Chebyshev inequality is extended to the problem of the probability of multiple inequalities for events with more than one variable. The corresponding two-sided Cantelli inequality is extended in a similar manner. The results for the linear combination of several variables are also given as their special cases.

Suggested Citation

  • Haruhiko Ogasawara, 2019. "The multiple Cantelli inequalities," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(3), pages 495-506, September.
    • Handle: RePEc:spr:stmapp:v:28:y:2019:i:3:d:10.1007_s10260-019-00452-2
    DOI: 10.1007/s10260-019-00452-2
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    References listed on IDEAS

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    1. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    2. Loperfido, Nicola, 2013. "Skewness and the linear discriminant function," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 93-99.
    3. Simai He & Jiawei Zhang & Shuzhong Zhang, 2010. "Bounding Probability of Small Deviation: A Fourth Moment Approach," Mathematics of Operations Research, INFORMS, vol. 35(1), pages 208-232, February.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. Marco Corazza & Florence Legros & Cira Perna & Marilena Sibillo, 2017. "Mathematical and Statistical Methods for Actuarial Sciences and Finance," Post-Print hal-01776135, HAL.
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    Cited by:

    1. Roxana A. Ion & Chris A. J. Klaassen & Edwin R. van den Heuvel, 2023. "Sharp inequalities of Bienaymé–Chebyshev and Gauß type for possibly asymmetric intervals around the mean," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(2), pages 566-601, June.
    2. Bhat, M. Ashraf & Kosuru, G. Sankara Raju, 2022. "Generalizations of some concentration inequalities," Statistics & Probability Letters, Elsevier, vol. 182(C).

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