On a Scheme of Sampling of Two Units With Inclusion Probability Proportional to Size

This paper introduces an unequal probability sampling without replacement scheme with inclusion probability proportional to size. This new scheme possesses some desirable properties with regard to pi(i) and pi(ij), and provides a non-negative variance estimator of the Horvitz and Thompson estimator, when the values of the auxiliary variable fulfill some restrictions. On comparing the suggested scheme with some of the existing sampling schemes in respect of efficiency and stability of the variance estimator empirically, it has been observed that the performance of the scheme is satisfactory.