A linear algorithm for generating random numbers with a given distribution

Let ξ be a random variable over a finite set with an arbitrary probability distribution. Improvements to a fast method of generating sample values for ξ 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)