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 language | English |
|---|---|
| Pages (from-to) | 1869-1885 |
| Number of pages | 17 |
| Journal | Taiwanese Journal of Mathematics |
| Volume | 17 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 2013 Nov 22 |
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All Science Journal Classification (ASJC) codes
- Mathematics(all)
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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 journal › Article
TY - JOUR
T1 - Stable poisson convergence for integer-valued random variables
AU - Cheng, Tsung-Lin
AU - Yang, Shun Yi
PY - 2013/11/22
Y1 - 2013/11/22
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=84887830946&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84887830946&partnerID=8YFLogxK
U2 - 10.11650/tjm.17.2013.1751
DO - 10.11650/tjm.17.2013.1751
M3 - Article
VL - 17
SP - 1869
EP - 1885
JO - Taiwanese Journal of Mathematics
JF - Taiwanese Journal of Mathematics
SN - 1027-5487
IS - 6
ER -