Poisson Limit Theorems for Number of Given Value Cells in Non-Homogeneous Generalized Allocation Scheme

2019 ◽  
Vol 40 (5) ◽  
pp. 614-623
Author(s):  
D. E. Chickrin ◽  
A. N. Chuprunov ◽  
P. A. Kokunin
Keyword(s):  
Limit Theorems ◽  
Allocation Scheme ◽  
Poisson Limit ◽  
Generalized Allocation Scheme

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 Poisson law for the distribution of the number of components in generalized allocation scheme

2019 ◽  
Vol 29 (4) ◽  
pp. 255-266 ◽  
Author(s):  
Aleksandr N. Timashev
Keyword(s):  
Sufficient Conditions ◽  
Rooted Trees ◽  
Allocation Scheme ◽  
Number Of Components ◽  
Poisson Law ◽  
Generalized Allocation Scheme

Abstract We consider problems on the convergence of distributions of the total number of components and numbers of components with given volume to the Poisson law. Sufficient conditions of such convergence are given. Our results generalize known statemets on the limit Poisson laws of the number of components (cycles, unrooted and rooted trees, blocks and other structures) in the corresponding generalized of allocation schemes.

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.

Compound Poisson limit theorems for Markov chains

1997 ◽  
Vol 34 (1) ◽  
pp. 24-34 ◽  
Author(s):  
Shoou-Ren Hsiau
Keyword(s):  
Markov Chain ◽  
Limit Theorem ◽  
Markov Chains ◽  
Limit Theorems ◽  
Compound Poisson ◽  
Poisson Limit

This paper establishes a compound Poisson limit theorem for the sum of a sequence of multi-state Markov chains. Our theorem generalizes an earlier one by Koopman for the two-state Markov chain. Moreover, a similar approach is used to derive a limit theorem for the sum of the k th-order two-state Markov chain.

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