Close-Point Spatial Tests and Their Application to Random Number Generators
Close-Point Spatial Tests and Their Application to Random Number Generators
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近点空间测试及其在随机数生成器中的应用
DOI：
10.1287/opre.48.2.308.12385
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
Richard J. Simard
中科院分区：
文献类型：
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作者：
P. L'Ecuyer;J. Cordeau;Richard J. Simard
对于k维单位超立方体或单位环面上均匀生成的点，我们研究了基于最近点对之间的L p距离的均匀性统计检验。不同的对在距离不超过，福特= 0，是一个随机过程，其初始部分，经过适当的变换和asn？8，是一个单位速率的渐近泊松过程。由于边缘效应，一旦ask超过2或3，在超立方体中收敛到这个渐近是缓慢的，但是在环面中是相当快的。我们看看他们的渐近分布的测试统计的确切分布的近似质量，讨论计算问题，并将测试应用到随机数生成器。线性全等发生器一旦接近周期长度的平方根，就会决定性地失败某些测试变体。
We study statistical tests of uniformity based on theL p -distances between them nearest pairs of points, forn points generated uniformly over thek-dimensional unit hypercube or unit torus. The number of distinct pairs at distance no more thant, fort = 0, is a stochastic process whose initial part, after an appropriate transformation and asn ? 8, is asymptotically a Poisson process with unit rate. Convergence to this asymptotic is slow in the hypercube as soon ask 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 asn approaches the square root of the period length.