Topic
Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: Asymptotic formulas are obtained for the partition function of the generalized multiclass Engset model which has applications to ISDN design and to current I/O computer architectures and a good accuracy is obtained even when these numbers are of order 10.
Abstract: Asymptotic formulas are obtained for the partition function of the generalized multiclass Engset model which has applications to ISDN design and to current I/O computer architectures. The derivation of the asymptotic expansion is based on an integral representation of the partition function in complex space through its generating function and evaluation of the integral by the saddle point method. The generating function is also used to derive an efficient exact recursive algorithm. Numerical results show that the accuracy of the asymptotic approximation increases when the number of sources in all classes and the number of servers grow simultaneously. Moreover, a good accuracy is obtained even when these numbers are of order 10.
17 citations
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17 citations
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17 citations
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TL;DR: In this article, the authors demonstrate that well-constructed error bounds for asymptotic approximations can provide useful analytical insight into the nature and reliability of the approximati...
Abstract: The purpose of this paper is to demonstrate that well-constructed error bounds for asymptotic approximations can provide useful analytical insight into the nature and reliability of the approximati...
17 citations
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TL;DR: In this article, with the aid of the branching theory of nonlinear equations, a coarse asymptotics of the probabilities of large deviations for integral statistics of the form======¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯) were derived for the two-sampled variants of these statistics.
Abstract: Part I has been published in the collection “Studies in the Theory of Probability Distributions. IV” (Zap. Nauchn. Sem. Leningr. Otd. Mat. Inst., Vol. 85), Leningrad, 1979, pp. 175–187. With the aid of the methods of the branching theory of nonlinear equations, one finds a coarse asymptotics of the probabilities of large deviations for integral statistics of the form
, which are generalizations of the Cramer-von Mises-Smirnov
statistic, and also for the twosample variants of these statistics. The obtained results allow us to compute the local exact Bahadur relative asymptotic efficiency. One establishes that the latter coincides with both the Bahadur approximate and the Pitman efficiencies.
17 citations