Random Number Generation Method Research Articles

Another method for random number generation on microcomputers

The random number generator u(t + 1) = u(t) 513 mod 235 is suitable for simulation work on microcomputers. Results of statistical tests of this generator show that it has reasonable properties. It can easily be implemented either in PASCAL or in assembly language.

An economical method for random number generation and a normal generator

A generalization of the Walker's method is presented for the case of continuous distributions. The proposed method is similar to the rejection technique but makes use of all the generated values. Application of the method for a normal random number generator of Kinderman and Ramage resulted in an algorithm that is equivalent to the FL5 procedure of Ahrens and Dieter.

A Program for Econometric and Spectral Analysis-EAS

and FORTRAN IV which is designed to accommodate most researchers' everyday econometric needs. However, this program is particularly useful when spectral methods are combined (in an ex post sense) with regression and simultaneous equations estimation., Residuals from regression or simultaneous equations estimation are easily saved by EAS and used in later spectral computations by using only two program statements.1 All spectral computations are highly efficient since the fast Fourier transform techniques developed by Cooley and Tukey [2] are used throughout. The program also allows algebraic expressions to be used directly in regression statements to define dependent or independent variables. Hence, special regression equations like the harmonic analysis model can be easily estimated with a single program statement. A partial enumeration of the program's capabilities is as follows: ordinary and weighted least squares regression; multivariate regression and estimation of Zellner's seemingly unrelated regression system; structural estimation of simultaneous equations by two-stage least squares, three-stage least squares, limited information maximum likelihood, k-class, double k-class, h-class, and Nagar's minimum bias k-class methods; power spectrum analysis, cross spectrum analysis, and simple frequency domain regression; random number generation and Monte Carlo methods; principal components analysis; estimation of partially nonlinear models by likelihood search techniques; and estimation of certain distributed lag models by Dhrymes' [3] methods. The program accommodates problems in which the sample size and number of yariables do not exceed 32,767 and 1,823, respectively, but the dynamic core allocation features of PL/1 are used to economize on all smaller problems. The design of the program is especially useful when a large data bank (subject to the abQve limitations) is to be maintained, updated, and periodically accessed for various types of econometric analyses. Most small- to medium-sized

The mixed method of random number generation: A tutorial

For the user who desires to construct his own random number generator we have presented guidelines and design considerations for implementing the mixed congruential method. The mixed generator is illustrated using several different languages and machines. We feel that by adhering to these guidelines, a user should be able to construct a random number generator that is adequate for most applications.

Monte Carlo Method for Evaluation of Transducer Critical Components and Transducer Characteristics

In the design and production of underwater acoustic transducers, two problems may arise. First, how does the design engineer specify the transducer component properties and their tolerances to best produce a cost effective transducer? Second, how does the production engineer determine if received transducer components will produce the desired quantity of acceptable transducers? The importance of these problems increases rapidly as the volume and production rate increase. This paper presents a Monte Carlo simulation capable of predicting the statistical variability of transducer characteristics from component variability data. The simulation consists of a power residue method of random number generation, a two-tailed chi-square test to insure that the numbers are random, a procedure which divides the probability density function of a component's property into equal area sections (equal chance for selection of property value) and a mathematical representation of the transducer. The simulation randomly chooses properties for the desired transducer components from their given (or assumed) distribution and generates the resulting transducer characteristics. Repetition of this procedure (Monte Carlo method) generates a series of random transducers which can be used to define the statistical variability of the desired transducer characteristic. An example of the results obtained using the simulation is presented.