
Digital Library of the
European Council for Modelling and Simulation 
Title: 
VarianceMean Mixtures As Asymptotic Approximations 
Authors: 
Victor Korolev, Vladimir Bening, Andrey Gorshenin, Maria Grigoryeva,
Alexander Zeifman 
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: 
Victor
Korolev, Vladimir Bening,
Andrey Gorshenin, Maria Grigoryeva, Alexander Zeifman (2014). VarianceMean Mixtures As Asymptotic
Approximations, ECMS 2014 Proceedings edited by: Flaminio
Squazzoni, Fabio Baronio,
Claudia Archetti, Marco Castellani European
Council for Modeling and Simulation. doi:10.7148/20140596 
DOI: 
http://dx.doi.org/10.7148/20140596 
Abstract: 
We present a general
transfer theorem for random sequences with independent random indexes in the double
array limit setting. We also prove its partial inverse providing necessary
and sufficient conditions for the convergence of randomly indexed random
sequences. Special attention is paid to the cases of random sums of
independent not necessarily identically distributed random variables and
statistics constructed from samples with random sizes. Using simple momenttype
conditions we prove the theorem on convergence of the distributions of such
sums to normal variancemean 
Full
text: 