  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.
