A bound on Poisson approximation for independent binomial random variables

2015 ◽  
Vol 9 ◽  
pp. 235-238
Author(s):  
K. Teerapabolarn
Keyword(s):  
Random Variables ◽  
Poisson Approximation ◽  
Binomial Random Variables

scholarly journals New Bounds on Poisson Approximation for Random Sums of Independent Binomial Random Variables}

2018 ◽  
Vol 7 (4) ◽  
pp. 43
Author(s):  
Giang Truong Le
Keyword(s):  
Random Variables ◽  
Poisson Approximation ◽  
Random Sums ◽  
Binomial Random Variables

In this paper, we use the Stein-Chen method to obtain new bounds on Poisson approximation for random sums of  independent binomial random variables. Some results related to sums of independent binomial distributed random variables are also investigated. The received results in the present study are more general and sharper than some known results.

On improvements of the order of approximation in the Poisson limit theorem

1996 ◽  
Vol 33 (01) ◽  
pp. 146-155 ◽  
Author(s):  
K. Borovkov ◽  
D. Pfeifer
Keyword(s):  
Limit Theorem ◽  
Random Variables ◽  
Poisson Approximation ◽  
Order Of Approximation ◽  
Operator Semigroups ◽  
Bernoulli Random Variables ◽  
Usual Rate ◽  
Poisson Limit ◽  
Poisson Measures ◽  
Special Case

In this paper we consider improvements in the rate of approximation for the distribution of sums of independent Bernoulli random variables via convolutions of Poisson measures with signed measures of specific type. As a special case, the distribution of the number of records in an i.i.d. sequence of length n is investigated. For this particular example, it is shown that the usual rate of Poisson approximation of O(1/log n) can be lowered to O(1/n 2). The general case is discussed in terms of operator semigroups.

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