Poisson approximation for random sums of Bernoulli random variables

1991 ◽  
Vol 11 (2) ◽  
pp. 161-165 ◽  
Author(s):  
Nikos Yannaros
Keyword(s):  
Random Variables ◽  
Poisson Approximation ◽  
Random Sums ◽  
Bernoulli Random Variables

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.

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

1996 ◽  
Vol 33 (1) ◽  
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/n2). The general case is discussed in terms of operator semigroups.

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.

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