AbstractThis paper is devoted to random-bit simulation of probability densities, supported on {[0,1]}. The term “random-bit” means that the source of randomness for simulation is a sequence of symmetrical Bernoulli trials. In contrast to the pioneer paper [D. E. Knuth and A. C. Yao,
The complexity of nonuniform random number generation,
Algorithms and Complexity,
Academic Press, New York 1976, 357–428], the proposed method demands the knowledge of the probability density under simulation, and not the values of the corresponding distribution function. The method is based on the so-called binary decomposition of the density and
comes down to simulation of a special discrete distribution to get several principal bits of output, while further bits of output are produced by “flipping a coin”.
The complexity of the method is studied and several examples are presented.
Sequential estimation of functions of $p$ for Bernoulli trials