Partially-Sampled Random Numbers for Accurate Sampling of Continuous Distributions

This page describes partially-sampled random numbers (incomplete numbers whose contents are determined only when necessary) and how they can be used to generate uniform and non-uniform random numbers to an arbitrary precision and with user-specified error bounds, while avoiding floating-point arithmetic. The page includes a new sampler for beta-distributed random numbers (with both parameters 1 or greater) and algorithms to compare and sample "e-rands", or partially-sampled exponential random numbers. This page contains Python code for beta and e-rand samplers, describes a generalization to sampling continuous distributions supported on the interval [0, 1], shows that the beta and continuous Bernoulli distributions are special cases of this generalization, and shows correctness test results and an application to weighted random sampling of a data stream of unknown size.