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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: 978-0-9564944-8-1

 

28th European Conference on Modelling and Simulation,

Brescia, Italy, May 27th – 30th, 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:10.7148/2014-0590

DOI:

http://dx.doi.org/10.7148/2014-0590

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 heavy-tailed alternative to stable laws.

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