ISSN:
1435-926X
Keywords:
Key words: Camp-Meidell inequality
;
CDF
;
Chebyshev inequality
;
Confidence interval
;
Density
;
Mean absolute deviation
;
Permutations
;
Poisson
;
Primes
;
Spherically symmetric
;
zeta function
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s184-000-8316-9
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