The SURVEYSELECT Procedure
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 i in stratum h equals
![\[ P_{hi} = Z_{hi} \bigl ( 1 + K_ h - (Z_{hi}/(1-Z_{hi}) \bigr ) \]](images/statug_surveyselect0096.png){kind=small}
where 
and
![\[ K_ h = \sum _{j=1}^{N_ h} \bigl ( Z_{hj} / ( 1 - Z_{hj} ) \bigr ) \]](images/statug_surveyselect0097.png){kind=small}
Murthy’s algorithm first selects a unit with probability 
. Then a second unit is selected from the remaining units with probability 
, where unit i is the first unit selected. The joint selection probability for units i and j in stratum h equals
![\[ P_{h(ij)} = Z_{hi} Z_{hj} \left( \frac{2 - Z_{hi} - Z_{hj}}{(1-Z_{hi}) (1-Z_{hj})} \right) \]](images/statug_surveyselect0099.png){kind=small}
See Cochran (1977, pp. 263–265) and Murthy (1957) for details.