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On chi-square type distributions with geometric degrees of freedom in relation to geometric sums

Tran Loc Hung 1, *
  1. University of Finance and Marketing
Correspondence to: Tran Loc Hung, University of Finance and Marketing. Email: tlhung@ufm.edu.vn.
Volume & Issue: Vol. 22 No. 1 (2019) | Page No.: 180-184 | DOI: 10.32508/stdj.v22i1.1053
Published: 2019-03-31

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Copyright The Author(s) 2023. This article is published with open access by Vietnam National University, Ho Chi Minh city, Vietnam. This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0) which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited. 

Abstract

The chi-square distribution with degrees of freedom has an important role in probability, statistics and various applied fields as a special probability distribution. This paper concerns the relations between geometric random sums and chi-square type distributions whose degrees of freedom are geometric random variables. Some characterizations of chi-square type random variables with geometric degrees of freedom are calculated. Moreover, several weak limit theorems for the sequences of chi-square type random variables with geometric random degrees of freedom are established via asymptotic behaviors of normalized geometric random sums.

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