Estimation of Finite Population Mean in Multivariate Stratified Sampling in the Presence of Non-response under Gamma Cost Function Using Different Allocation Techniques

Abstract

In practical utilization of stratified random sampling scheme, the investigator meets a problem to select a sample that maximizes the precision of a finite population mean under cost constraint. An allocation of sample size becomes complicated when more than one characteristic is observed from each selected unit in a sample. In many real-life situations, a linear cost function of sample sizes nh and uh are not a good approximation to actual cost of sample survey when traveling or other related cost between selected units in a stratum is significant. In this paper, sample allocation problem in multivariate stratified random sampling in the presence of non-response with proposed cost function is formulated into nonlinear multi objective mathematical programming. A solution procedure is proposed using extended lexicographic goal programming approach. A numerical example is presented to illustrate the computational details and to compare the efficiency of Extended Lexicographic goal programming and compromise allocation. In this multi-objective non-linear integer programming problem, we use Individual optimum allocation technique, Goal programming and Extended Lexicographic Goal programming for solution purposes. To illustrate the application, we apply this formulation on a real data set.