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Many random variables can be approximated quite closely by c(M + U1 + U2 + U3), where c is constant, M is a discrete random variable, and the U's are uniform random variables. Such a representation appears attractive as a method for generating variates in a computer, since M + U1 + U2 + U3 can be quickly and simply generated. A typical application of this idea will have M taking from 4 to 7 values; the required X will be produced in the form c(M + U1 + U2 + U3) perhaps 95--99% of the time, and occasionally by the rejection technique, to make the resulting distribution come out right. This paper describes the method and gives examples of how to generate beta, normal, and chi-square variates.
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George Marsaglia (1966) studied this question.