
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:
9780993244025 30^{th}
European Conference on Modelling and Simulation, Regensburg Germany, May 31^{st}
– June 3^{rd}, 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:10.7148/20160669 
DOI: 
http://dx.doi.org/10.7148/20160669 
Abstract: 
Statistical regularities of the
information flows in contemporary communication, computational and other
information systems are characterized be the presence of the socalled “heavy
tails”. The outlying observations make the traditional momenttype location
estimators inaccurate. In this case the robust mediantype 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 heavytailed 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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