The permutation distribution induced upon a finite population by the order of selection under successive sampling is closely related to the order statistics of independent exponentially distributed waiting times. This characterization is applied to obtain necessary and sufficient conditions for asymptotic normality of the sum of characteristics observed in a successive sample from a finite population. The necessary and sufficient conditions generalize previous results for simple random sampling without replacement, and apply to sampling fractions close to 0 or 1.
"Successive Sampling in Large Finite Populations." Ann. Statist. 11 (2) 702 - 706, June, 1983. https://doi.org/10.1214/aos/1176346175