Poisson Limit Theorems in an Allocation Scheme with an Even Number of Particles in Each Cell

2020 ◽  
Vol 41 (3) ◽  
pp. 289-297
Author(s):  
F. A. Abdushukurov ◽  
A. N. Chuprunov
Keyword(s):  
Limit Theorems ◽  
Allocation Scheme ◽  
Poisson Limit ◽  
Number Of Particles

A Poisson limit theorem for incomplete symmetric statistics

1983 ◽  
Vol 20 (01) ◽  
pp. 47-60 ◽  
Author(s):  
M. Berman ◽  
G. K. Eagleson
Keyword(s):  
Limit Theorem ◽  
Limit Theorems ◽  
Random Variables ◽  
Asymptotic Distributions ◽  
Poisson Limit ◽  
Symmetric Statistics ◽  
Limit Result ◽  
Independent Identically Distributed

Silverman and Brown (1978) have derived Poisson limit theorems for certain sequences of symmetric statistics, based on a sample of independent identically distributed random variables. In this paper an incomplete version of these statistics is considered and a Poisson limit result shown to hold. The powers of some tests based on the incomplete statistic are investigated and the main results of the paper are used to simplify the derivations of the asymptotic distributions of some statistics previously published in the literature.

Rates of Poisson convergence for U-statistics

1979 ◽  
Vol 16 (2) ◽  
pp. 428-432 ◽  
Author(s):  
T. C. Brown ◽  
B. W. Silverman
Keyword(s):  
Rate Of Convergence ◽  
Limit Theorems ◽  
Plane Region ◽  
U Statistics ◽  
Poisson Limit ◽  
Special Case

Poisson limit theorems for U-statistics are studied. A general rate of convergence is obtained; this rate is improved for the special case where the U-statistic arises from the consideration of distances between uniformly distributed points in a well-behaved plane region.

Limit Theorems for Number of Particles from a Fixed Set of Cells

2019 ◽  
Vol 40 (5) ◽  
pp. 624-629
Author(s):  
D. E. Chickrin ◽  
A. N. Chuprunov ◽  
P. A. Kokunin
Keyword(s):  
Limit Theorems ◽  
Fixed Set ◽  
Number Of Particles

Short distances, flat triangles and Poisson limits

1978 ◽  
Vol 15 (04) ◽  
pp. 815-825 ◽  
Author(s):  
Bernard Silverman ◽  
Tim Brown
Keyword(s):  
Spatial Data ◽  
Limit Theorems ◽  
Nearest Neighbour ◽  
Poisson Limit

Motivated by problems in the analysis of spatial data, we prove some general Poisson limit theorems for the U-statistics of Hoeffding (1948). The theorems are applied to tests of clustering or collinearities in plane data; nearest neighbour distances are also considered.

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