Stable poisson convergence for integer-valued random variables

Tsung-Lin Cheng, Shun Yi Yang

Research output: Contribution to journalArticle

Abstract

In this paper, we obtain some stable Poisson Convergence Theorems for arrays of integer-valued dependent random variables. We prove that the limiting distribution is a mixture of Poisson distribution when the conditional second moments on a given σ-algebra of the sequence converge to some positive random variable. Moreover, we apply the main results to the indicator functions of rowise interchangeable events and obtain some interesting stable Poisson convergence theorems.

Original languageEnglish
Pages (from-to)1869-1885
Number of pages17
JournalTaiwanese Journal of Mathematics
Volume17
Issue number6
DOIs
Publication statusPublished - 2013 Nov 22

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Convergence Theorem
Siméon Denis Poisson
Random variable
Indicator function
Dependent Random Variables
Integer
Poisson distribution
Limiting Distribution
Moment
Converge
Algebra

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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Stable poisson convergence for integer-valued random variables. / Cheng, Tsung-Lin; Yang, Shun Yi.

In: Taiwanese Journal of Mathematics, Vol. 17, No. 6, 22.11.2013, p. 1869-1885.

Research output: Contribution to journalArticle

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