A stratified modified probability proportional to size sampling technique.

In Probability Proportional to Size (PPS) sampling, size variable associated with the sampling unit leads to the probability selection of units proportional to its size. In the literature, modification to PPS has been proposed by dividing the population in two groups on arranging the units in decreasing order of their frequency. We introduce Stratified Modified Probability Proportional to Size with Replacement (Stratified MPPSWR) sampling and Stratified Modified Rao-Hartley-Cochran (Stratified MRHC) design in case of without replacement sampling where the data are distributed in homogeneous strata such that it follows Zipf's law within each stratum and the units are selected using MPPSWR and MRHC design respectively. In proposed schemes, each stratum is divided into two groups and first group is selected into the sample with probability 1 and units from second group are selected using PPSWR and RHC sampling respectively as in MPPSWR and MRHC sampling design. The relative efficiency of the proposed schemes is carried out and an illustration is given using the real data set. The proposed sampling schemes are seen to be more efficient than existing techniques. [ABSTRACT FROM AUTHOR]