
Digital Library of the
European Council for Modelling and Simulation 
Title: 
Transfer Theorem Concerning Asymptotic Expansions For The Distribution
Functions Of Statistics Based On Samples With Random Sizes 
Authors: 
Vladimir Bening, Vladislav A. Savushkin, Egor I. Shunkov, Alexander Zeifman, Victor Korolev 
Published in: 
(2014).ECMS 2014 Proceedings edited
by: Flaminio Squazzoni,
Fabio Baronio, Claudia Archetti,
Marco Castellani European Council for
Modeling and Simulation. doi:10.7148/2014 ISBN:
9780956494481 28^{th}
European Conference on Modelling and Simulation, Brescia,
Italy, May 27^{th} – 30^{th},
2014 
Citation
format: 
Vladimir
Bening, Vladislav A. Savushkin, Egor I. Shunkov, Alexander Zeifman,
Victor Korolev (2014). Transfer Theorem Concerning Asymptotic Expansions For The Distribution
Functions Of Statistics Based On Samples With Random Sizes, ECMS 2014
Proceedings edited by: Flaminio Squazzoni,
Fabio Baronio, Claudia Archetti,
Marco Castellani European Council for Modeling and Simulation. doi:10.7148/20140590 
DOI: 
http://dx.doi.org/10.7148/20140590 
Abstract: 
In the paper, we discuss the
transformation of the asymptotic expansion for the distribution of a
statistic admitting Edgeworth expansion if the
sample size is replaced by a random variable.We
demonstrate that all those statistics that are regarded as asymptotically normal
in the classical sense, become asymptotically Laplace or Student if the
sample size is random. Thus, the Laplace and Student distributions may be
used as an asymptotic approximation in descriptive statistics being a
convenient heavytailed alternative to stable laws. 
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