Poisson approximation

1994 ◽  
pp. 92-102
Author(s):  
Gunnar Blom ◽  
Lars Holst ◽  
Dennis Sandell
Keyword(s):  
Poisson Approximation

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.

Some Elementary Results on Poisson Approximation in a Sequence of Bernoulli Trials

SIAM Review ◽  
1978 ◽  
Vol 20 (3) ◽  
pp. 567-579 ◽  
Author(s):  
R. J. Serfling
Keyword(s):  
Poisson Approximation ◽  
Bernoulli Trials

scholarly journals The lower tail: Poisson approximation revisited

2015 ◽  
Vol 48 (2) ◽  
pp. 219-246 ◽  
Author(s):  
Svante Janson ◽  
Lutz Warnke
Keyword(s):  
Poisson Approximation ◽  
Lower Tail

Poisson approximation for a sum of dependent indicators: an alternative approach

2002 ◽  
Vol 34 (03) ◽  
pp. 609-625 ◽  
Author(s):  
N. Papadatos ◽  
V. Papathanasiou
Keyword(s):  
Total Variation ◽  
Upper Bound ◽  
Random Variables ◽  
Random Variable ◽  
Poisson Approximation ◽  
Total Variation Distance ◽  
Poisson Random Variable ◽  
Birthday Problem ◽  
Alternative Approach ◽  
Variation Distance

The random variablesX1,X2, …,Xnare said to be totally negatively dependent (TND) if and only if the random variablesXiand ∑j≠iXjare negatively quadrant dependent for alli. Our main result provides, for TND 0-1 indicatorsX1,x2, …,Xnwith P[Xi= 1] =pi= 1 - P[Xi= 0], an upper bound for the total variation distance between ∑ni=1Xiand a Poisson random variable with mean λ ≥ ∑ni=1pi. An application to a generalized birthday problem is considered and, moreover, some related results concerning the existence of monotone couplings are discussed.

scholarly journals Non-abelian correction to the Poisson approximation for multi-gluon bremsstrahlung

2017 ◽  
Vol 802 ◽  
pp. 012010
Author(s):  
Andriniaina N. Rasoanaivo ◽  
W. A. Horowitz
Keyword(s):  
Poisson Approximation ◽  
Gluon Bremsstrahlung

scholarly journals Poisson approximation of the length spectrum of random surfaces

2018 ◽  
Vol 67 (3) ◽  
pp. 1115-1141
Author(s):  
Bram Petri ◽  
Christoph Thaele
Keyword(s):  
Poisson Approximation ◽  
Length Spectrum ◽  
Random Surfaces

Poisson Approximation

2012 ◽  
pp. 651-688
Author(s):  
Santosh S. Venkatesh
Keyword(s):  
Poisson Approximation
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