Linear Systematic Sampling with Unequal Sampling Intervals in the Presence of Linear Trend

The present paper deals with the linear systematic sampling with unequal sampling intervals in the presence of linear trend among the population values. As a result, explicit expressions for the linear systematic sample means with different random starts in a labelled population with linear trend for a pre-assigned fixed sample size and the population size together its variance are obtained. The efficiencies of the proposed linear systematic sampling with that of simple random sampling without replacement, linear systematic sampling and diagonal systematic sampling schemes are assessed algebraically and also for certain natural populations. It is observed that the proposed linear systematic sampling performs better than the sampling schemes mentioned above.