Tests of randomness for pseudorandom number generators

This study examined the “randomness” of the numbers generated by the VIC-20 computer. Using eight standard tests, it was determined that the numbers provided by the VIC-20 are adequately random for practical purposes. The tests are applicable to other computer systems and provide a general means for evaluating random-number generators.     

A theoretical and empirical comparison of mainframe,microcomputer, and pocket calculator pseudorandom number generators

This article presents an extensive theoretical and empirical analysis of the pseudorandom number generators provided by subroutine libraries (NAG, CERN, IMSL, and ESSL), statistical and simulation software packages (GLIM, SAS, SPSS, DATASIM, ESSP, and LLRANDOMII), builtin functions of programming languages (APL, Turbo Pascal, Advanced BASIC, GW-BASIC, and QBASIC), and autoimplemented algorithms (Fishman & Moore, 1986; Wichmann & Hill, 1982; Van Es, Gill, & Van Putten, 1983). On the basis of these analyses, it is concluded that most of the built-in functions of the software packages that were tested can be used safely. In addition, it is concluded that the Wichmann and Hill algorithm is a good choice if only single-precision arithmetic is available, but that a prime-modulus multiplicative congruential generator with modulus 2³¹ ?1 and multiplier 16,807 is a better choice if double-precision arithmetic is available, and that the same generator with multiplier 62,089,911 or 742,938,285 is the best choice if extended-precision arithmetic is available. A Turbo Pascal and a VS FORTRAN program for the latter are given in the Appendixes.     

NORMUL: A FORTRAN program for testing multivariate normality

NORMUL is a FORTRAN program that provides a test of whether data conform to a multivariate normal distribution. The method involves correlating Mahalanobis distances for observed data with expected chi-square percentile values. This obtained correlation is then tested for significance by empirically evaluating the probability of its belonging to a distribution generated from multivariate normal data.     

A Pascal version of a pseudorandom number generator

This article describes a random number generator routine based on a Pascal algorithm gested by Lewis and Payne (1973) and Payne (1973).