Best constants in Chebyshev inequalities with various applications |
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Authors: | Anirban DasGupta |
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Affiliation: | (1) Department of Statistics, Purdue University, West Lafayette, IN 47907, USA (e-mail: dasgupta@stat.purdue.edu), US |
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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. Received: April 1999 |
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Keywords: | : Camp-Meidell inequality CDF Chebyshev inequality Confidence interval Density Mean absolute deviation Permutations Poisson Primes Spherically symmetric zeta function |
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