A Skip-based Algorithm for Weighted Reservoir Random Sampling with Replacement

Reservoir sampling techniques can be used to extract a sample from a population of unknown size. Most of attention has been put to sampling without replacement, with only a small number of studies focusing on sampling with replacement. Specifically, to the author's knowledge, no one has explored in detail how to deal with the weighted case in this setting. In this work, we demonstrate that the results shown in [1] can be further generalized using similar techniques to develop a fast skip-based algorithm for weighted reservoir sampling with replacement.