#### PPS Sampling with Replacement

If you specify the METHOD=PPS_WR
option, PROC SURVEYSELECT selects units with probability proportional to size and with replacement. The procedure makes independent random selections from the stratum of units, selecting with probability . Because units are selected with replacement, a unit can be selected for the sample more than once. The expected number of
hits (selections) for unit i in stratum h is . If you specify the JTPROBS
option, PROC SURVEYSELECT computes the joint expected number of hits for all pairs of selected units in each stratum. The
joint expected number of hits for units i and j in stratum h is