Murthy’s PPS Method

Murthy’s method (METHOD=PPS_MURTHY) selects two units from each stratum, with probability proportional to size and without replacement. The selection probability for unit in stratum equals


where and


Murthy’s algorithm first selects a unit with probability . Then a second unit is selected from the remaining units with probability , where unit is the first unit selected. The joint selection probability for units and in stratum equals


See Cochran (1977, pp. 263–265) and Murthy (1957) for details.