On Moments of the Power Series Distributions
Identifiers and Pagination:Year: 2009
First Page: 3
Last Page: 6
Publisher Id: TOSPJ-1-3
Article History:Received Date: 8/10/2008
Revision Received Date: 23/10/2008
Acceptance Date: 10/11/2008
Electronic publication date: 15/1/2009
Collection year: 2009
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.
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.