Murthy's PPS Method

The SURVEYSELECT Procedure

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 i in stratum h equals

P_hi = Z_hi [ 1 + K - (Z_hi/(1-Z_hi) ]

where Z_hi = M_hi / M_{h ·} and

$K = \sum_{j=1}^N [ Z_{hj} / ( 1 - Z_{hj} ) ]$

Murthy's algorithm first selects a unit with probability Z_hi . Then a second unit is selected from the remaining units with probability Z_hj/(1-Z_hi), 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 [(2 - Z_hi - Z_hj)/((1-Z_hi) (1-Z_hj))]

Murthy's method requires that the relative size Z_hi be less than 0.5 for all units. Refer to Cochran (1977, pp. 263 -265) and Murthy (1957).

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