Estimation of Population Mean in the Presence of Linear Trend

Abstract

The present article deals with some methods for estimation of finite populations means in the presence of linear trend among the population values. As a result, we provided a strategy for the selection of sampling interval k for the case of circular systematic sampling, which ensures better estimator for the population mean compared to other choices of the sampling interval. This has been established based on empirical studies. Further we more, applied multiple random starts methods for selecting random samples for the case of linear systematic sampling and diagonal systematic sampling schemes. We also derived the explicit expressions for the variances and their estimates. The relative performances of simple random sampling, linear systematic sampling and diagonal systematic sampling schemes with single and multiple random starts are also assessed based on numerical examples.

Keywords:

• Circular Systematic sampling
• Diagonal systematic sampling
• Linear systematic sampling
• Multiple random starts
• Simple random sampling
• Linear trend
• Trend free sampling

Mathematics Subject Classification:

• 62D05

Acknowledgments

The authors wish to thank the editor and the reviewer for their comments and suggestions which have helped to improve the presentation of this article.