scholarly journals On a bound of the absolute constant in the Berry–Esseen inequality for i.i.d. Bernoulli random variables

2018 ◽  
Vol 5 (3) ◽  
pp. 385-410 ◽  
Author(s):  
Anatolii Zolotukhin ◽  
Sergei Nagaev ◽  
Vladimir Chebotarev
Keyword(s):  
Absolute Constant ◽  
Random Variables ◽  
Bernoulli Random Variables ◽  
The Absolute ◽  
Esseen Inequality

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.

scholarly journals Distribution of Geometrically Weighted Sum of Bernoulli Random Variables

2011 ◽  
Vol 02 (11) ◽  
pp. 1382-1386 ◽  
Author(s):  
Deepesh Bhati ◽  
Phazamile Kgosi ◽  
Ranganath Narayanacharya Rattihalli
Keyword(s):  
Random Variables ◽  
Weighted Sum ◽  
Bernoulli Random Variables

scholarly journals A conditional Berry–Esseen inequality

2019 ◽  
Vol 56 (01) ◽  
pp. 76-90
Author(s):  
Thierry Klein ◽  
Agnés Lagnoux ◽  
Pierre Petit
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Random Variables ◽  
Esseen Inequality ◽  
Independent And Identically Distributed

AbstractAs an extension of a central limit theorem established by Svante Janson, we prove a Berry–Esseen inequality for a sum of independent and identically distributed random variables conditioned by a sum of independent and identically distributed integer-valued random variables.

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