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Abstract

The geometric sums have been arisen from the necessity to resolve practical problems in ruin prob- ability, risk processes, queueing theory and reliability models, etc. Up to the present, the results related to geometric sums like asymptotic distributions and rates of convergence have been investigated by many mathematicians. However, in a lot of various situations, the results concerned domains of geometric attraction are still limitative. The main purpose of this article is to introduce concepts on the domain of geometric attraction of standard Laplace distribution. Using method of characteristic functions, the necessary and sufficient conditions for a probability distribution belongs to the domain of geometric attraction of standard Laplace distribution are shown. In special case, obtained result is a weak limit theorem for geometric sums of independent and identically distributed random variables which has been well-known as the second central limit theorem. Furthermore, based on the obtained results of this paper, the analogous results for the domains of geometric attraction of exponential distribution and Linnik distribution can be established. More generally, we may extend results to the domain of geometric attraction of geometrically strictly stable distributions.


 


 


 



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Article Details

Issue: Vol 22 No 1 (2019)
Page No.: 143-146
Published: Mar 29, 2019
Section: Natural Sciences - Research article
DOI: https://doi.org/10.32508/stdj.v22i1.1049

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Creative Commons License

Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Loc Hung, T., & Kien, P. (2019). The necessary and sufficient conditions for a probability distribution belongs to the domain of geometric attraction of standard Laplace distribution. Science and Technology Development Journal, 22(1), 143-146. https://doi.org/https://doi.org/10.32508/stdj.v22i1.1049

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