Some limit theorems for dependent Bernoulli random variables

2021 ◽  
Vol 170 ◽  
pp. 109010
Author(s):  
Renato J. Gava ◽  
Bruna L.F. Rezende
Keyword(s):  
Limit Theorems ◽  
Random Variables ◽  
Bernoulli Random Variables

Limit theorems for correlated Bernoulli random variables

2008 ◽  
Vol 78 (15) ◽  
pp. 2339-2345 ◽  
Author(s):  
Barry James ◽  
Kang James ◽  
Yongcheng Qi
Keyword(s):  
Limit Theorems ◽  
Random Variables ◽  
Bernoulli Random Variables

scholarly journals Random sums of random vectors and multitype families of productive individuals

2004 ◽  
Vol 2004 (19) ◽  
pp. 975-990
Author(s):  
I. Rahimov ◽  
H. Muttlak
Keyword(s):  
Stochastic Processes ◽  
Special Form ◽  
Limit Theorems ◽  
Random Variables ◽  
Random Sums ◽  
Random Vectors ◽  
Bernoulli Random Variables

We prove limit theorems for a family of random vectors whose coordinates are a special form of random sums of Bernoulli random variables. Applying these limit theorems, we study the number of productive individuals inn-type indecomposable critical branching stochastic processes with types of individualsT1,…,Tn.

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.

A central limit theorem by remainder term for renewal processes

1992 ◽  
Vol 24 (2) ◽  
pp. 267-287 ◽  
Author(s):  
Allen L. Roginsky
Keyword(s):  
Central Limit Theorem ◽  
Limit Theorem ◽  
Central Limit ◽  
Remainder Term ◽  
Limit Theorems ◽  
Random Variables ◽  
Central Limit Theorems ◽  
Renewal Processes

Three different definitions of the renewal processes are considered. For each of them, a central limit theorem with a remainder term is proved. The random variables that form the renewal processes are independent but not necessarily identically distributed and do not have to be positive. The results obtained in this paper improve and extend the central limit theorems obtained by Ahmad (1981) and Niculescu and Omey (1985).

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