Algorithm-I on splitting of sizes for sampling procedure with inclusion probabilities proportional to size

Abstract

The sampling scheme proposed by Srivastava and Singh depends upon a specific split of the sizes and most of the πij′s do not satisfy the condition of non-negativity of variance estimates as suggested by Hanurav. Using the information about the nature of non-negativity condition (фij>0) approach, Dwivedi provided split of sizes with less number of trials which gives a set of πij ′s satisfying the condition of non-negativity of variance estimates. This paper provides an algorithm for a proper split of sizes which gives a set of πij ′s such that the condition of non-negativity of variance estimates is nearly satisfied. It is also shown that on an average the relative efficiency of proposed algorithm shows the superiority over PPSWR.