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A Linear Algorithm for Generating Random Numbers with a Given Distribution
September 1991 (vol. 17 no. 9)
pp. 972-975

Let xi be a random variable over a finite set with an arbitrary probability distribution. Improvements to a fast method of generating sample values for xi in constant time are suggested. The proposed modification reduces the time required for initialization to O(n). For a simple genetic algorithm, this improvement changes an O(g n 1n n) algorithm into an O(g n) algorithm (where g is the number of generations, and n is the population size).

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[2] D. E. Knuth,The Art of Computer Programming, 2nd ed. Reading, MA: Addison-Wesley, 1981, pp. 115-116.
[3] J. K. Moss, R. J. Simpson, and W. Tempest, "A pseudo-random pulse train generator with controllable rate for modeling of audiometric systems,"Radio and Electron. Eng., vol. 42, pp. 419-424, 1970.
[4] A. J. Walker, "An efficient method for generating discrete random variables with general distributions,"ACM Trans. Math Software, vol. 3, no. 3, pp. 253-256, 1977.

Index Terms:
linear algorithm; random numbers; random variable; finite set; arbitrary probability distribution; simple genetic algorithm; genetic algorithms; probability; random number generation
Citation:
M.D. Vose, "A Linear Algorithm for Generating Random Numbers with a Given Distribution," IEEE Transactions on Software Engineering, vol. 17, no. 9, pp. 972-975, Sept. 1991, doi:10.1109/32.92917
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