Uniform Random Number Generator Research Articles

A random number generator based on the combination of four LCGs

A portable package for uniform random number generation is proposed, based on a backbone generator with period length near 2 121, which combines four linear congruential generators. The package provides for multiple (virtual) generators evolving in parallel. Each generator has many disjoint subsequences, and software tools are provided to reset the state of any generator to the beginning of its first, previous, or current subsequence. An implementations is given in the C language.

An improved deterministic algorithm for generating different many-element random samples

We consider the problem of deterministically selecting s uniformly random different m-element subsets of (1), h., k. The only known lower bound for the time to solve this problem is the trivial Ω(sm). The best two previously known solutions are of time O( sm 3 log m log log m) and O( s( k + m)), respectively. In this paper we present an algorithm whose time complexity is O( s 2 m 2 + sm 2 log m log log m + sm log sm). Thus, for s < m log m log log m this algorithm is the fastest known deterministic algorithm. The main idea of the algorithm is using a uniform random number generator to efficiently construct biased random numbers.

Adaptive fuzzy frequency hopper

An adaptive fuzzy system generates the frequency hopping sequence for a spread spectrum communications system. The system learns rules from data and acts as a pseudorandom number generator. The IMSL uniform random number generator gives training samples. An adaptive scheme learns associations between previous samples and the current sample and encodes these as fuzzy rules. The output fuzzy set for each rule acts as a conditional probability density function. The if-part of the rule states the conditions. At each step thirty prior outputs, scanned according to a fixed sampling pattern, give a new sample distribution x/sub k/. The vector x/sub k/ partially matches the if-part distribution of a fuzzy rule and partially fires that rule's output fuzzy set. With the estimated output fuzzy sets the fuzzy system computes the conditional density p/sub . >

The microcomputer performance of uniform variate random number generators expressed in FORTRAN

The microcomputer performance of random number generators is an important component of uncertainty analysis in environmental modeling. The results of a performance study of 110 uniform variate pseudo-random number generators expressed in FORTRAN are presented. The algorithms tested include multiplicative, mixed, additive and quadratic congruential generators plus example combined and generalized feedback shift register generators. Results are presented for generator speed, period, and 17 statistical measures of number randomness quality. These results indicate that, based on both speed and number quality, the multiplicative linear congruential generator can yield superior performance. Specific moduli and multipliers are recommended for this generator. For relatively low period generators, explicit use of the integer modulus function provides superior performance. When high period generators are implemented, they should be based on the Schrage (1979) or Bongiovanni (1987) computational procedure for accomplishing the modulus operation with arithmetic that avoids explicit use of the modulus function.

An n-Dimensional Uniform Random Number Generator Suitable for IBM-Compatible Microcomputers

The uniform random number generator is the basic building block used in computer-based Monte Carlo and simulation studies. Mixed congruential random number generators, such as those intrinsic to MS-DOS or PC-DOS BASIC, have a number of shortcomings that make them unsuitable in multidimensional studies. A random number generator that overcomes these shortcomings is the generalized feedback shift register generator, an algorithm well documented for mainframe use. It can be used in a microcomputer environment and implemented in BASIC.

Designing a Uniform Random Number Generator Whose Subsequences are k-Distributed

A method for designing a uniform random number generator based on M-sequence is described. It generates a k-distributed sequence $\{ x_t ;t = 0,1,2, \cdots \} $ such that its decimated sequences $\{ x_{nt} ;t = 0,1,2, \cdots \} $ are also k-distributed for several values of n. The sequence is obtained by permuting the bits in Tausworthe sequence; a suitable permutation is found by solving a special $0 - 1$ integer linear programme, a set covering problem. The constraint matrix of the programme is obtained by applying a modified Gaussian elimination to another $0 - 1$ matrix. Two simple heuristic algorithms for the programme are given and demonstrated to find good approximate solutions to an illustrative example.

Note on a Proposed Test for Random Number Generators

A recently proposed test for uniform random number generators is based on the mean and variance of the outcome of a sequence of iterations. This note points out that many nonuniform random number generators would pass such a test, and derives an improved test based on the exact distribution of the outcome.

Generating artificial traffic over a local area network using random number generators

Effective testing and performance evaluation of a local area computer network requires the ability to generate artificial traffic. This in turn requires algorithms for generating random number sequences. This article evaluates several random number generation algorithms considered for emulating traffic over NBSNET, a local area computer network at the National Bureau of Standards. The algorithms are evaluated in light of certain time, space, and programming constraints dictated by NBS's application. The table-based method, using an additive uniform random number generator for selection from the table, was determined to be a satisfactory method considering NBSNET's constraints, and is being used to generate artificial traffic for continuing local network research experimentation.

Mortalité du sapin baumier défolié par la tordeuse des bourgeons de l'épinette dans la région de la Gatineau au Québec

This paper presents a method of analysis which differentiates between spruce budworm caused mortality and regular mortality on balsam fir in the Gatineau region in Quebec. A first attempt was made using multiple linear regression and a uniform random number generator. In order to overcome the bias inherent to the least squares method when dealing with a binary (0,1) dependent variable, a profit analysis was also conducted. In this case, the parameters and their variance were estimated using likehood method. These two approaches proved to be equivalent when percent budworm caused mortality was compared within the 1958 to 1979 period covered by the data at hand, while the outbreak lasted from 1968 to 1975.In 1979, approximately 55% of the stems had been killed by the budworm, accounting for 53% of the volume. Maple-yellow birch associations were more affected than fir associations although no significant difference was found. Fir mortality was delayed by aerial spraying of insecticides but this advantage disappeared as soon as the spray operations came to an end.

A statistical check of the DECsystem-10 FORTRAN pseudorandom number generator

The pseudorandom number generator in the FORTRAN library (function RAN) of the DECsystem-10 was tested for the statistical properties of an independent uniform random number generator. Five statistical tests were employed: the frequency test, serial test, lagged product test, test of runs up and down, and test of runs above and below the mean. The generator passed all tests. It was concluded that it could be used in applications that require a sequence of uniformly distributed random numbers.

Additive vs multiplicative uniform pseudo-random number generators in the generation of Erlang variates

This paper presents the comparative results of several test runs involving the use of several unit uniform random number generators with an inverse transform to generate Erland random variates with λ=1 and k = 3, 4, 5, and 6. The results show that two commonly used generators (a multiplicative and a mixed one) produce unacceptable results. Two others (an additive one and a multiplicative one) produce acceptable results. The computer system used is an IBM 370/3033.

Uniform random number generator

The recent flurry of random number routines and your continued plea for material had led me to dust off my favorite trick uniform random number generator. It requires no seed, produces numbers uniformly distributed between 0 and 1, is acyclic and for all practical purposes, is completely unpredictable and irreproducible.

Random-number generators

A commonly used uniform random-number generator is examined in light of a genetic-simulation problem. Although this generator is often useful, it proves defective in this case. The author suggests that any proposed generator be checked for the properties needed by the simulation problem at hand.

A Uniform Random Number Generator Based on the Combination of Two Congruential Generators

A method of generating pseudo-random uniform numbers based on the combination of two congruential generators is described. It retains two of the desirable features of congruential generators, namely, the long cycle and the case of implementation on a digital computer. Furthermore, unlike the method of combining congruential generators recently proposed by MacLaren and Marsaglia, it does not require the retention in computer memory of a table of generated numbers. The generator gave completely satisfactory results on a fairly stringent series of statistical tests.

Fourier Analysis of Uniform Random Number Generators

A method of analysis of uniform random number generators is developed, applicable to almost all practical methods of generation. The method is that of Fourier analysis of the output sequences of such generators. With this tool it is possible to understand and predict relevant statistical properties of such generators and compare and evaluate such methods. Many such analyses and comparisons have been carried out. The performance of these methods as implemented on differing computers is also studied. The main practical conclusions of the study are: (a) Such a priori analysis and prediction of statistical behavior of uniform random number generators is feasible. (b) The commonly used multiplicative congruence method of generation is satisfactory with careful choice of the multiplier for computers with an adequate (≥ ∼ 35-bit) word length. (c) Further work may be necessary on generators to be used on machines of shorter word length.

Numerical Simulation of Stationary and Non-Stationary Gaussian Random Processes

The purpose of this paper is to present numerical methods for the computation of samples of a Gaussian random process x(t) with prescribed autocorrelation or power spectral density.