The Annals of Probability

A Compound Poisson Convergence Theorem

Y. H. Wang

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Abstract

In 1971, Simons and Johnson showed that the classical theorem of binomial to Poisson convergence is actually stronger than in the usual sense. Their result was proved valid also for the distributions of sums of independent, but not necessarily identically distributed, Bernoulli random variables by Chen in 1974. Here we show that their result is indeed true for a much larger class of random variables. The limiting distribution is generalized to a compound Poisson distribution.

Article information

Source
Ann. Probab., Volume 19, Number 1 (1991), 452-455.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176990555

Digital Object Identifier
doi:10.1214/aop/1176990555

Mathematical Reviews number (MathSciNet)
MR1085347

Zentralblatt MATH identifier
0745.60019

JSTOR
links.jstor.org

Subjects
Primary: 60F15: Strong theorems
Secondary: 60F05: Central limit and other weak theorems

Keywords
Sum of random variables limiting distributions modes of convergence binomial Poisson compound Poisson

Citation

Wang, Y. H. A Compound Poisson Convergence Theorem. Ann. Probab. 19 (1991), no. 1, 452--455. doi:10.1214/aop/1176990555. https://projecteuclid.org/euclid.aop/1176990555


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