On the correct implementation of the Hanurav-Vijayan selection procedure for unequal probability sampling without replacement

The Hanurav-Vijayan procedure belongs to the class of exact, draw-by-draw algorithms for unequal probability sampling without replacement. This procedure has been implemented in market-leading commercial statistical packages such as SAS/STAT and SPSS, which have popularized its use. Unfortunately, the description of the Hanurav-Vijayan procedure in the documentation of these softwares is partially flawed, propagating errors issued from the statistical literature. Besides, despite it is often used, this procedure has almost fallen in oblivion in the literature devoted to sampling probability designs, and no comparisons were made with other competing methods. It is the purpose of the present paper to rehabilitate the Hanurav-Vijayan procedure by correctly describing its implementation details and providing some basic elements of comparison with the well-known Rao-Sampford procedure.