A modified regression-cum-ratio estimator for finite population mean in presence of nonresponse using ranked set sampling

Several situations arise where decision-making is required for some characteristics of an asymmetrical population for example estimation of the weekly number of server breakdowns at a company. The estimation methods based upon classical sampling designs are not suitable in such situations and some specialized methods and/or estimators are required. The ranked set sampling is a procedure that is suitable in such situations. In this paper, a new estimator is proposed that can be used to estimate population characteristics in case of asymmetrical populations. The proposed estimator is useful for estimation of population mean in the presence of non-response in study variable by using ranked set sampling procedure. The estimator is based upon two auxiliary variables to reduce the effect of asymmetry. The use of two auxiliary variables is also helpful in minimizing the variation in the estimation of the population mean of the study variable. The ranked set sampling procedure is used to get better accuracy as the actual measurements may be time-consuming, expensive, or difficult to obtain in a small sample size. The use of ranked set sampling also reduces the effect of asymmetry in the characteristics under study. The expressions for the mean square error and bias for the proposed estimators have been derived. The performance of the proposed estimator is evaluated by using real-life data and a simulation study is carried out to get an overview of efficiency. The relative efficiency of the proposed estimator is compared with some existing estimators. It has been found that the proposed estimator is highly efficient as compared with Mohanty's regression cum ratio estimator in simple random sampling and is more reliable in the case of non-response with a small sample size.