Random number generation testing

An empirical test of this possibility was performed by computing values of the variance of the two terms in equation 44-77. The Normal random number generator of MATLAB was used to create multiple values of Normally distributed random numbers for Er and Es these were plugged into the two expressions of equation 44-77 and the variance computed. Values between 100 and 106 were used in each computation of the variance. 

PK tests with a high-speed random number generator. 

International Business Machines Corporation, "Random Number Generation and Testing, Manual G20-8011, IBM Corporation, White Plains, New York. 

After completing the computation of the mean Ky° and KyC and standard deviations, a random number generator was used to develop 1,000 normally distributed values of each Kv° and Kv°, having the listed standard deviations. Verification of the normality of the randomly generated number sets was done by a Chi-square test on each number set. 

IV. Testing Random Number Generators A. Parallel Tests... 

We shall focus here on developments caused by widespread use of parallel computers to perform Monte Carlo calculations. Our impression is that individual users are porting random number generators to parallel computers in an ad hoc fashion, possibly unaware of some of the issues that come to the fore when massive calculations are performed. Parallel algorithms can probe other qualities of random number generators such as interprocess correlation. A recent review covers parallel random number generation in somewhat more depth [12]. The interested reader can also refer to Refs. 13-17 for work related to parallel random number generation and testing. 

We have recently developed a library implementing several of the parallel random number generators and statistical tests of them on the most widely available multiprocessor computers. Documentation and software are available at... 

We now mention some tests of parallel random number generators. 

P. Coddington, Tests of Random Number Generators Using Ising Model Simulations, Int. J. Mod. Phys. C 7(3), 295-303 (1996). 

We present results for two- and three-descriptor models addition of a fourth descriptor yielded no significant improvement in predictive accuracy. In the two-descriptor case there are only 276 possible input combinations, so we examine each explicitly, whereas, in the three-descriptor case there are 2024, so we use the genetic algorithm (GA) to optimize the descriptor selection. Use of the GA in the two-descriptor case gives models of comparable quality to the exhaustive search, but this test of the algorithm is not very stringent because the space of input combinations is small. Because both the GA and the NN depend on the random number generator seed, several trials were performed in each case (as detailed in Section IV.D.2). 

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