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.

Short distances, flat triangles and Poisson limits

1978 ◽  
Vol 15 (4) ◽  
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.

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.

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.

Random walks and periodic continued fractions

1985 ◽  
Vol 17 (1) ◽  
pp. 67-84 ◽  
Author(s):  
Wolfgang Woess
Keyword(s):  
Random Walks ◽  
Harmonic Functions ◽  
Limit Theorems ◽  
Continued Fraction ◽  
Transition Probabilities ◽  
Local Limit ◽  
Periodic Sequence ◽  
Nearest Neighbour ◽  
Continued Fraction Expansions ◽  
Local Limit Theorems

Nearest-neighbour random walks on the non-negative integers with transition probabilities p0,1 = 1, pk,k–1 = gk, pk,k+1 = 1– gk (0 < gk < 1, k = 1, 2, …) are studied by use of generating functions and continued fraction expansions. In particular, when (gk) is a periodic sequence, local limit theorems are proved and the harmonic functions are determined. These results are applied to simple random walks on certain trees.

scholarly journals K-NEAREST NEIGHBOUR QUERY PERFORMANCE ANALYSES ON A LARGE SCALE TAXI DATASET: POSTGRESQL VS. MONGODB

2019 ◽  
Vol XLII-2/W13 ◽  
pp. 1531-1538 ◽  
Author(s):  
İ. B. Coşkun ◽  
S. Sertok ◽  
B. Anbaroğlu
Keyword(s):  
New York ◽  
Spatial Data ◽  
Large Scale ◽  
Information Science ◽  
Spatial Information ◽  
Database Management System ◽  
Nearest Neighbour ◽  
Spatial Accuracy ◽  
K Value ◽  
Spatial Information Science

<p><strong>Abstract.</strong> The increasing volume of transport network data necessitates the use of a DataBase Management System (DBMS) to store, query and analyse data. There are two main types of DBMS: relational and non-relational. Many different DBMS are available on the market but only some of them could handle spatial data. Therefore, determining which DBMS to use for operational purposes is of interest to researchers and analysts working in spatial information science. One of the commonly used spatial queries in GIS is the k-Nearest Neighbour (kNN) of a given point. This paper analyses the performance of the kNN query in PostgreSQL and MongoDB, both being a representative of relational and NoSQL DBMS respectively. Two different metrics have been investigated to determine the performance: i) spatial accuracy and ii) run time. Haversine and Vincenty formulas are used to calculate the distance between the point and the determined neighbours, which are then used to determine the spatial accuracy of the DBMS. Sensitivity analysis have been carried out by varying the k value and the execution times are recorded. The experiments are carried out on New York City’s openly available taxi dataset consisting of millions of taxi pickup and dropoff points. The results indicate that MongoDB outperforms Postgres both in terms of execution time and spatial accuracy regardless the value of k. In order to facilitate reproducibility of the results, the developed software is shared on GitHub.</p>

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