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.
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The author is indebted to the comments of the reviewers, which have led to some additional findings and improvements of an earlier version of this paper. This work was partially supported by a Grant-in-Aid for Scientific Research from the Japanese Ministry of Education, Culture, Sports, Science and Technology (JSPS KAKENHI, Grant No.17K00042).
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Ogasawara, H. The multiple Cantelli inequalities. Stat Methods Appl 28, 495–506 (2019). https://doi.org/10.1007/s10260-019-00452-2
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DOI: https://doi.org/10.1007/s10260-019-00452-2