Generalisation of Das & Mohanty Sampling Scheme

Abstract

This paper revisits and extends the Das & Mohanty sampling scheme, which integrates Probability Proportional to Size (PPS) systematic sampling 
with Simple Random Sampling Without Replacement (SRSWOR). After outlining the foundations of PPS sampling by Hansen and Hurwitz (1943) 
and the Horvitz–Thompson (1952) framework, the study proposes a generalised scheme based on a Bernoulli trial with weight w, allowing controlled 
mixing of PPS and SRSWOR. Analytical derivations of inclusion probabilities and variances are presented, with empirical illustrations across three 
test populations. The findings indicate that the proposed scheme approximates πPS sampling for small w, yielding reduced variance in certain cases 
(notably for populations B and C), though slightly less efficient for population A. This highlights the adaptability of the generalised approach and 
its potential to outperform classical estimators under specific population structures where auxiliary variables are strongly correlated with the study 
variable.