Sparse Serial Tests of Uniformity for Random Number Generators
Sparse Serial Tests of Uniformity for Random Number Generators
复制标题
随机数生成器均匀性的稀疏串行测试
DOI：
10.1137/s1064827598349033
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发表时间：
1998
期刊：
影响因子：
--
通讯作者：
S. Wegenkittl
中科院分区：
文献类型：
--
作者：
P. L'Ecuyer;Richard J. Simard;S. Wegenkittl
研究了检验(伪随机数)产生器产生的连续值向量的一致性和独立性的不同形式的序列检验。这些测试将t维单位超立方体划分为k个等体积的立方体单元，在该超立方体中生成n个点(向量)，计算每个单元中有多少个点，并计算测试统计量，该测试统计量被定义为应用于这k个单独计数器的某个单变量函数f的值的总和。同时考虑了重叠向量和非重叠向量。对于线性同余、Tausworthe、非线性逆等不同的生成元族，比较了这些函数和k的不同选择方法，得到了拒绝独立均匀随机变量的零假设所需(估计)样本量的公式，它是生成元周期长度的函数。对于对应于线性生成器的备选方案类，最有效的测试结果是$k\ggn$(与模拟书籍中通常所做或推荐的相反)，并使用重叠的向量。
Different versions of the serial test for testing the uniformity and independence of vectors of successive values produced by a (pseudo)random number generator are studied. These tests partition the t-dimensional unit hypercube into k cubic cells of equal volume, generate n points (vectors) in this hypercube, count how many points fall in each cell, and compute a test statistic defined as the sum of values of some univariate function f applied to these k individual counters. Both overlapping and nonoverlapping vectors are considered. For different families of generators, such as linear congruential, Tausworthe, nonlinear inversive, etc., different ways of choosing these functions and of choosing k are compared, and formulas are obtained for the (estimated) sample size required to reject the null hypothesis of independent uniform random variables, as a function of the period length of the generator. For the classes of alternatives that correspond to linear generators, the most efficient tests turn out to have $k \gg n$ (in contrast to what is usually done or recommended in simulation books) and to use overlapping vectors.