caa a22 4500 475793196 CHVBK 20180406123716.0 cr unu---uuuuu 170329e20000901xx s 000 0 eng 10.1007/s184-000-8316-9 doi (NATIONALLICENCE)springer-10.1007/s184-000-8316-9 DasGupta Anirban Department of Statistics, Purdue University, West Lafayette, IN 47907, USA (e-mail: dasgupta@stat.purdue.edu), US aut Best constants in Chebyshev inequalities with various applications [Elektronische Daten] [Anirban DasGupta] 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. Springer-Verlag Berlin Heidelberg, 2000 Key words: Camp-Meidell inequality nationallicence CDF nationallicence Chebyshev inequality nationallicence Confidence interval nationallicence Density nationallicence Mean absolute deviation nationallicence Permutations nationallicence Poisson nationallicence Primes nationallicence Spherically symmetric nationallicence zeta function nationallicence https://doi.org/10.1007/s184-000-8316-9 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s184-000-8316-9 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- DasGupta Anirban Department of Statistics, Purdue University, West Lafayette, IN 47907, USA (e-mail: dasgupta@stat.purdue.edu), US aut Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer