Abstract.
In this article we describe some ways to significantly improve the Markov-Gauss-Camp-Meidell inequalities and provide specific applications. We also describe how the improved bounds are extendable to the multivariate case. Applications include explicit finite sample construction of confidence intervals for a population mean, upper bounds on a tail probability P(X>k) by using the density at k, approximation of P-values, simple bounds on the Riemann Zeta function, on the series , improvement of Minkowski moment inequalities, and construction of simple bounds on the tail probabilities of asymptotically Poisson random variables. We also describe how a game theoretic argument shows that our improved bounds always approximate tail probabilities to any specified degree of accuracy.
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Received: April 1999
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DasGupta, A. Best constants in Chebyshev inequalities with various applications. Metrika 51, 185–200 (2000). https://doi.org/10.1007/s184-000-8316-9
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DOI: https://doi.org/10.1007/s184-000-8316-9