On Using the Box‐Muller Transformation with Multiplicative Congruential Pseudo‐Random Number Generators

S. C. Chay, R. D. Fardo and M. Mazumdar

Journal of the Royal Statistical Society Series C, 1975, vol. 24, issue 1, 132-135

Abstract: In a recent paper, Neave has observed that the agreement between the observed and the expected frequencies is poor in the two tails of a normal distribution when the random normal deviates are generated by a multiplicative congruential scheme: xr+1 = bxr (mod M). In this note we show that for the particular example considered by Neave, the difficulty can be removed by reversing the order of the members of the pairs of successive pseudo‐random numbers obtained from this generator and then using them in Box–Muller's formula. An explanation for the observed agreement resulting from this permutation is then given in the light of Neave's analysis.

Date: 1975
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