RESEARCH ARTICLE


On Moments of the Power Series Distributions



Slavko Simic*
Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia.


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© 2009 Simic et al.;

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Mathematical Institute SANU, Kneza Mihaila 36, 11000 Belgrade, Serbia. E-mail: ssimic@turing.mi.sanu.ac.yu


Abstract

For the Power Series Distributions generated by an arbitrary entire function of finite order, applying methods of Karamata’s Theory of Regular Variation, we obtain asymptotic behavior of its moments. As an illustration, we calculate the moments of distributions generated by the class of Mittag-Leffler functions of which the well-known Poisson Law is just a special case.

Keywords: Distribution moments, entire functions of finite order, regular variation, karamata..