线性同余人字映射组合产生均匀随机数

研究了线性同余法与人字映射组合随机数发生器 :xn=Axn-1(mod M) ,wn=2 xn,　 xn≤ 0 .5 M,wn=2 (M-xn) +1 ,　 xn>0 .5 M,yn=wn/ M.该组合发生器比相应的线性同余法在空间结构上有明显改善 ,并通过统计检验     

伪随机数串叠加的渐近理论

用单一方式产生的伪随机数串,其随机性常不够理想。讨论当将大量这种串按同余的意义叠加时,其结果的渐近性态,得出了能收敛到真正的随机性的充要条件。     

随机数生成

本文讨论最有用的给定概率密度函数情形下的随机数生成问题,借助几何概率描述舍选法。     

基于泊松对相关的伪随机数发生器的统计测试方法

测试伪随机数发生器(pseudo random number generator,PRNG)的性能是一个非常重要的问题,通常以能否通过检验均匀性和独立性的统计测试方法来衡量.1998年Rudnick和Sarnak提出了[0,1)上实数序列的泊松对相关(Poissonian pair correlations,PPC)的概念,独立且均匀分布的实数序列满足泊松对相关.该文基于泊松对相关的概念提出了一种测试(0,1)中伪随机数序列的一级统计测试方法,给出了收敛判别标准的选取方法,并对常见的PRNG(线性同余发生器、Mersenne Twister、Matlab.rand函数以及基于无理数π重叠产生的PRNG等)进行了测试,同时与卡方检验、序列检验、游程检验以及自相关检验进行比较.结果表明该测试方法不仅简单灵活、可操作性和可移植性较强,能有效地同时检验伪随机数序列的均匀性和独立性.     

部分随机数测试标准的物理意义及其硬件改进措施

随机数在密码学、保密通信和国家安全等领域具有重要的作用,因此寻求一种提高随机数测试通过率的方法具有重要意义.对美国NIST SP800-22测试标准中的部分测试标准进行了分析,并针对其中的单比特频数测试、游程测试、块内最大游程测试以及子块测试分别给出了其物理意义和改进随机数发生器性能的硬件措施.     

S-PLUS与Visual C++随机数发生器性质的比较

本文通过对统计软件S-PLUS和Visual C++6.0自带的随机数发生器产生的一定数量的随机数进行参数检验、均匀性检验、独立性检验以及周期检验后, 发现S-PLUS产生的随机数列均匀性、独立性以及周期明显地优于VC++.     

随机数与模拟实验

在统计与概率学习中,最有效的教学途径是通过学生亲身实践、动手模拟,来体会统计思想和概率的意义．随机模拟试验需要大量随机数,用手工方法费时费力,而图形计算器可以快捷便利地实现,笔者以HP图形计算器为例,探讨利用图形计算器进行随机数与模拟实验教学的问题．     

舍选法几何解释及曲边梯形概率密度随机数生成算法

本文首先从几何概率角度看舍选法的直观意义,找出改进舍选法的途径;然后讨论梯形和曲边梯形概率密度随机数生成算法,给出若干简单概率密度随机数生成实例。     

一般组合逆同余法的算法与偏差分析

本文研究了逆同余产生伪随机数的方法，给出了一般的组合逆同余法算法．将已有结果进行理论比较，得到了一个较好的伪随机数序列的产生方法．     

关于组合最优化理论的多媒体教学实践

本文讨论和分析了开发组合最比化理论系列课程多媒体课件的基本认识、课件的主要特色和体会，并提出了使用多媒体课件中应注意的问题．     

Orbits and Lattices for Linear Random Number Generators with Composite Moduli

In order to analyze certain types of combinations of multiple recursive linear congruential generators (MRGs), we introduce a generalized spectral test. We show how to apply the test in large dimensions by a recursive procedure based on the fact that such combinations are subgenerators of other MRGs with composite moduli. We illustrate this with the well-known RANMAR generator. We also design an algorithm generalizing the procedure to arbitrary random number generators.

     

A Method of Systematic Search for Optimal Multipliers in Congruential Random Number Generators

This paper presents a method of systematic search for optimal multipliers for congruential random number generators. The word-size of computers is a limiting factor for development of random numbers. The generators for computers up to 32 bit word-size are already investigated in detail by several authors. Some partial works are also carried out for moduli of 2⁴⁸ and higher sizes. Rapid advances in computer technology introduced recently 64 bit architecture in computers. There are considerable efforts to provide appropriate parameters for 64 and 128 bit moduli. Although combined generators are equivalent to huge modulus linear congruential generators, for computational efficiency, it is still advisable to choose the maximum moduli for the component generators. Due to enormous computational price of present algorithms, there is a great need for guidelines and rules for systematic search techniques. Here we propose a search method which provides ‘fertile’ areas of multipliers of perfect quality for spectral test in two dimensions. The method may be generalized to higher dimensions. Since figures of merit are extremely variable in dimensions higher than two, it is possible to find similar intervals if the modulus is very large. This revised version was published online in July 2006 with corrections to the Cover Date.     

Distribution Properties of Multiply-with-Carry Random Number Generators

We study the multiply-with-carry family of generators proposed by Marsaglia as a generalization of previous add-with-carry families. We define for them an infinite state space and focus our attention on the (finite) subset of recurrent states. This subset will, in turn, split into possibly several subgenerators. We discuss the uniformity of the -dimensional distribution of the output of these subgenerators over their full period. In order to improve this uniformity for higher dimensions, we propose a method for finding good parameters in terms of the spectral test. Our results are stated in a general context and are applied to a related complementary multiply-with-carry family of generators.

     

Random Number Generators

Journal of the Operational Research Society -     

Maximally Equidistributed Combined Tausworthe Generators

Tausworthe random number generators based on a primitive trinomial allow an easy and fast implementation when their parameters obey certain restrictions. However, such generators, with those restrictions, have bad statistical properties unless we combine them. A generator is called maximally equidistributed if its vectors of successive values have the best possible equidistribution in all dimensions. This paper shows how to find maximally equidistributed combinations in an efficient manner, and gives a list of generators with that property. Such generators have a strong theoretical support and lend themselves to very fast software implementations.

     

非均匀随机数产生

本文详细介绍了产生非均匀随机数的一般方法,常用连续分布(正态分布,Gamma分布,Beta分布,χ2分布和F分布)的抽样法及利用R软件产生随机数的方法。     

Design of Practical and Provably Good Random Number Generators

We present a construction for a family of pseudo-random generators that are very fast in practice, yet possess provable statistical and cryptographic unpredictability properties. Such generators are useful for simulations, randomized algorithms, and cryptography.Our starting point is a slow but high quality generator whose use can be mostly confined to a preprocessing step. We give a method of stretching its outputs that yields a faster generator. The fast generator offers smooth memory–time–security trade-offs and also has many desired properties that are provable. The slow generator can be based on strong one-way permutations or block ciphers. Our implementation based on the block cipher DES is faster than popular generators.     

随机数及其在数据库中的应用

本文在分析随机数及其产生方法的基础上 ,介绍计算机产生随机数和随机抽样在数据库中应用的实现方法     

Asymptotic Expansions for the Distribution of the Crossing Number of a Strip by Sample Paths of a Random Walk

The complete asymptotic expansions are obtained for the distribution of the crossing number of a strip in n steps by sample paths of an integer-valued random walk with zero mean. We suppose that the Cramer condition holds for the distribution of jumps and the width of strip increases together with n; the results are proven under various conditions on the width growth rate. The method is based on the Wiener–Hopf factorization; it consists in finding representations of the moment generating functions of the distributions under study, the distinguishing of the main terms of the asymptotics of these representations, and the subsequent inversion of the main terms by the modified saddle-point method.