scholarly journals Asymptotics and Sharp Bounds in the Poisson Approximation to the Poisson-Binomial Distribution

Bernoulli ◽  
1999 ◽  
Vol 5 (6) ◽  
pp. 1021 ◽  
Author(s):  
Bero Roos
Keyword(s):  
Binomial Distribution ◽  
Poisson Approximation ◽  
Sharp Bounds ◽  
Poisson Binomial Distribution

scholarly journals On moderate deviations in Poisson approximation

2020 ◽  
Vol 57 (3) ◽  
pp. 1005-1027
Author(s):  
Qingwei Liu ◽  
Aihua Xia
Keyword(s):  
Random Graphs ◽  
Binomial Distribution ◽  
Poisson Approximation ◽  
Moderate Deviations ◽  
Tail Probabilities ◽  
Matching Problem ◽  
Birthday Problem ◽  
Occupancy Problem ◽  
Poisson Binomial Distribution ◽  
The Right

AbstractIn this paper we first use the distribution of the number of records to demonstrate that the right tail probabilities of counts of rare events are generally better approximated by the right tail probabilities of a Poisson distribution than those of the normal distribution. We then show that the moderate deviations in Poisson approximation generally require an adjustment and, with suitable adjustment, we establish better error estimates of the moderate deviations in Poisson approximation than those in [18]. Our estimates contain no unspecified constants and are easy to apply. We illustrate the use of the theorems via six applications: Poisson-binomial distribution, the matching problem, the occupancy problem, the birthday problem, random graphs, and 2-runs. The paper complements the works [16], [8], and [18].

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