Close-point spatial tests and their application to random number generators
成果类型：
Article
署名作者：
L'Écuyer, P; Cordeau, JF; Simard, R
署名单位：
Universite de Montreal
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.48.2.308.12385
发表日期：
2000
页码：
308-317
关键词：
摘要：
We study statistical tests of uniformity based on the L-p-distances between the m nearest pairs of points, for n points generated uniformly over the k-dimensional unit hypercube or unit torus. The number of distinct pairs at distance no more than t, for t greater than or equal to 0, is a stochastic process whose initial part, after an appropriate transformation and as n --> infinity, is asymptotically a Poisson process with unit rate. Convergence to this asymptotic is slow in the hypercube as soon as k exceeds 2 or 3, due to edge effects, but is reasonably fast in the torus. We look at the quality of approximation of the exact distributions of the tests statistics by their asymptotic distributions, discuss computational issues, and apply the tests to random number generators. Linear congruential generators fail decisively certain variants of the tests as soon as n approaches the square root of the period length.