Article
Poisson approximation for random sums of Bernoulli random variables
Department of Mathematics, Royal Institute of Technology, S10044 Stockholm, Sweden
Statistics [?] Probability Letters (Impact Factor: 0.6). 02/1991; 11(2):161165. DOI: 10.1016/01677152(91)90135E ABSTRACT
Bounds for the total variation distance between the distribution of the sum of a random number of Bernoulli summands and an appropriate Poisson distribution are given. The results can be used to derive limit theorems with rates of convergence for marked and thinned point processes. Some examples are given.
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ABSTRACT: This paper gives a new bound for the total variation distance between the distribution of random sums of independent Bernoulli random variables and an appropriate Poisson distribution. The bound in this study is sharper than that reported in [2]. Two examples have been given to illustrate the result obtained. 
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Article: A new bound on pointwise Poisson approximation for random sums of Bernoulli random variables
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ABSTRACT: A new bound for the point metric between the distribution of random sums of independent Bernoulli random variables and an appropriate Poisson distribution is obtained. The bound in this study is sharper than those reported in [3]. 
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ABSTRACT: A nonuniform bound for the distance between the distribution of random sums of independent Bernoulli random variables and an appropriate Poisson distribution is obtained. It is sharper than the bound reported in [7].