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On Using the Box‐Muller Transformation with Multiplicative Congruential Pseudo‐Random Number Generators
Author(s) -
Chay S. C.,
Fardo R. D.,
Mazumdar M.
Publication year - 1975
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346711
Subject(s) - multiplicative function , mathematics , pseudorandom number generator , transformation (genetics) , random number generation , linear congruential generator , discrete mathematics , statistics , combinatorics , biology , physics , power (physics) , mathematical analysis , biochemistry , quantum mechanics , gene
Summary 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: x r +1 = bx r (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.