Communications of the ACM
Least squares quantization in PCM
IEEE Transactions on Information Theory
Continuous random variate generation by fast numerical inversion
ACM Transactions on Modeling and Computer Simulation (TOMACS)
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This paper presents methods to invert efficiently the distribution function of an arbitrary positive random variable. Such methods preserve the monotonic relationship between the random variable and the uniform deviate which generates it. This relationship is necessary to reduce the variance of an estimator in simulation experiments. For discrete distributions, an indexed search method is employed utilizing variable spaced cutpoints. For continuous distributions, a piecewise continuous increasing quadratic spline is fit to prespecified values of the inverse distribution function. The index number of the piece is then generated by the indexed search method. The spacing of the cutpoints for the search is chosen to minimize the expected number of comparisons required per variate generated.