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Digital Library

of the European Council for Modelling and Simulation

 

Title:

Variance-Mean 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: 978-0-9564944-8-1

 

28th European Conference on Modelling and Simulation,

Brescia, Italy, May 27th – 30th, 2014

Citation format:

Victor Korolev, Vladimir Bening, Andrey Gorshenin, Maria Grigoryeva, Alexander Zeifman (2014). Variance-Mean Mixtures As Asymptotic Approximations, ECMS 2014 Proceedings edited by: Flaminio Squazzoni, Fabio Baronio, Claudia Archetti, Marco Castellani  European Council for Modeling and Simulation. doi:10.7148/2014-0596

DOI:

http://dx.doi.org/10.7148/2014-0596

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 moment-type conditions we prove the theorem on convergence of the distributions of such sums to normal variance-mean

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