Marsaglia random number generator

The Marsaglia random number generator [Marsaglia et al. 1990] is known as a combination generator because it is constructed from two different generators. It has a period of about... 

Marsaglia G, A Zaman and W W Tsang 1990. Towards a Universal Random Number Generate Statistics and Probability Letters 8 35-39. 

G. Marsaglia, A Current View of Random Number Generators, in Computing Science and Statistics Proceedings of the XVIth Symposium on the Interface, 1985, pp. 3-10. 

Guamieri F and W C Still 1994. A Rapidly Convergent Simulation Method Mixed Monte Carlo/ Stochastic Dynamics. Journal of Computational Chemistry 151302-1310 Marsaglia G, A Zaman and W W Tsang 1990. Towards a Universal Random Number Generator Statistics and Probability Letters 8.35-39. 

Marsaglia, G., and Zaman, A. (1994). Some Portable Very-Long-Period Random Number Generators. Computers in Physics, 8(1) 117-121. 

However, a single statistical test is not adequate to verify the randomness of a sequence, because typical MCMC applications can be sensitive to various types of correlations. However, if the generator passes a wide variety of tests, then our confidence in its randomness increases. The tests suggested by Knuth [7] and those implemented in the DIEHARD package by Marsaglia [36] are a standard. Since there are many generators that pass these tests, there is no reason to consider one that is known to fail. (Of course, any generator will eventually fail most tests, so we always must state how many numbers were used in the test level of accuracy). 

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