Abstract
In this article we have proposed some ratio estimator for the study variable based on the linear combination of known values of Co-efficient of Skewness and Median of the auxiliary variable utilizing Rank set sampling and Simple random sampling are proposed. Mean squared error up to the first degree of approximation are derived. The proposed ratio estimators under rank set sampling perform better than the proposed ratio estimators under simple random sampling. The simulated study has been carried out in support of the results.
Highlights
In sample surveys most of the times, along with the variable of interest Y, information on auxiliary variable X, which is highly correlated with Y is collected
One such example is Ratio method of estimation which utilizes the information on auxiliary variable X, which is positively correlated with the variable of interest Y, with a view of improving the precision of the estimate of population mean
The procedure of ratio estimation under rank set sampling given by Samawi and Muttlak[1] are as under: Let Y be the variable if interest and X be a suitable concomitant variable which is correlated to Y and easy to rank
Summary
In sample surveys most of the times, along with the variable of interest Y, information on auxiliary variable X, which is highly correlated with Y is collected. To obtain a more efficient estimator of population mean through information on auxiliary variable is usually utilized. An alternative method to Simple Random Sampling (SRS) called Ranked Set Sampling (RSS) was introduced to increase the efficiency of the estimation of population mean[11]. There are cases in practical situation where the variable of interest Y is difficult to measure and to rank but a concomitant variable X, which is highly correlated with Y, can be ranked and be used for the ranking of the sampling units. Some extension is done by Samawi[1], who utilized both the rank and the measure of the concomitant variable and considered ratio estimation using RSS. The ratio estimation based on RSS is more efficient compared with the SRS ratio estimate
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