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Digital Library

of the European Council for Modelling and Simulation

 

Title:

Asymptotic Expansions For The Distribution Function Of The Sample Median Constructed From A Sample With Random Size

Authors:

Vladimir E. Bening, Victor Korolev, Alexander Zeifman

Published in:

 

 

(2016).ECMS 2016 Proceedings edited by: Thorsen Claus, Frank Herrmann, Michael Manitz, Oliver Rose, European Council for Modeling and Simulation. doi:10.7148/2016

 

 

ISBN: 978-0-9932440-2-5

 

30th European Conference on Modelling and Simulation,

Regensburg Germany, May 31st – June 3rd, 2016

 

Citation format:

Vladimir E. Bening, Victor Korolev, Alexander Zeifman (2016). Asymptotic Expansions For The Distribution Function Of The Sample Median Constructed From A Sample With Random Size, ECMS 2016 Proceedings edited by: Thorsten Claus, Frank Herrmann, Michael Manitz, Oliver Rose  European Council for Modeling and Simulation. doi:10.7148/2016-0669

 

DOI:

http://dx.doi.org/10.7148/2016-0669

Abstract:

Statistical regularities of the information flows in contemporary communication, computational and other information systems are characterized be the presence of the so-called “heavy tails”. The outlying observations make the traditional moment-type location estimators inaccurate. In this case the robust median-type location estimators are preferable. On the other hand, the random character of the intensity of the flow of informative events results in that the available sample size (traditionally this is the number of observations registered within a certain time interval) is random. The randomness of the sample size crucially changes the asymptotic properties of the estimators. In the paper, asymptotic expansions are obtained for the distribution function of the sample median constructed from a sample with random size. A general theorem on the asymptotic expansion is proved for this case. The cases of the Laplace, Student and Cauchy distributions are considered. Special attention is paid to the situations in which the heavy-tailed distributions (Cauchy, Laplace) are inherent in both the original sample and the asymptotic regularities of the sample median (Student, Laplace) due to the randomness of the sample size. This approach can be successfully used for big data mining and analysis of information flows in highperformance computing.

 

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