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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 |
Full
text: |