Fixing the Size of a Varying Probability Sample in a Direct and a Randomized Response Survey

In this chapter, our intention is to estimate the proportion of population in a community bearing a stigmatizing characteristic \(A\) . Suppose \(y\) is a stigmatizing variable defined on a finite population \(U = \left( {1,2, ..., i, ... N} \right)\) . This real variable \(y\) takes the values \(y_{i}\) which may be either 1 or 0 respectively for a person \(i\) in \(U\) bearing the sensitive feature \(A\) or its complement \(A^{c}\) .