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A chain ratio-type estimator is proposed for the estimation of finite population mean under systematic sampling scheme using two auxiliary variables. The mean square error of the proposed estimator is derived up to the first order of approximation and is compared with other relevant existing estimators. To illustrate the performances of the different estimators in comparison with the usual simple estimator, we have taken a real data set from the literature of survey sampling.

We have proposed a generalized class of exponential type estimators for population mean under the framework of systematic sampling using the knowledge of two auxiliary variables. The expressions for the mean square error of the proposed class of estimators have been corrected up to first order of approximation. Comparisons of the efficiency of the proposed class of estimators under the optimal conditions with the other existing estimators have been presented through a real secondary data. The statistical study provides strong evidence that the proposed class of estimators in survey estimation procedure results in substantial efficiency improvements over the other existing estimation approaches.

In this manuscript, we have proposed a difference-type estimator for population mean under two-phase sampling scheme using two auxiliary variables. The properties and the mean square error of the proposed estimator are derived up to first order of approximation; we have also found some efficiency comparison conditions for the proposed estimator in comparison with the other existing estimators under which the proposed estimator performed better than the other relevant existing estimators. We show that the proposed estimator is more efficient than other available estimators under the two phase sampling scheme for this one example; however, further study is needed to establish the superiority of the proposed estimator for other populations.

To obtain the best estimates of the unknown population parameters have been the key theme of the statisticians. In the present paper we have suggested some estimators which estimate the population parameters efficiently. In short we propose a ratio, product, and regression estimators using two auxiliary variables, when there are some maximum and minimum values of the study and auxiliary variables, respectively. The properties of the proposed strategies in terms of mean square errors (variances) are derived up to first order of approximation. Also the performance of the proposed estimators have shown theoretically and these theoretical conditions are verified numerically by taking four real data sets under which the proposed class of estimators performed better than the other previous works.

In this article, we have suggested a class of estimators for the estimation of the population variance of the variable of interest. The proposed estimators used some certain known information of the auxiliary variable, such as kurtosis, coefficient of variation, and the minimum and maximum values. The properties of the suggested class of estimators such as the bias and mean squared error (MSE) are obtained up to the first order of approximation. In order to check the performances of the estimators and to verify the theoretical results, we conducted a simulation study. The results of the simulation study show that the proposed class of estimators have lower MSE than other existing estimators. This holds for all simulation scenarios. In the application part, we used data from Statistical Bureau of Pakistan, and from the Textbook of Cochran, which also confirms that the suggested class of estimators is more efficient than the usual unbiased variance estimator, ratio estimator, traditional regression estimator, and other existing estimators in survey literature.

This paper presents a class of ratio-type estimators for the evaluation of finite population mean under maximum and minimum values by using knowledge of the auxiliary variable. The properties of the proposed estimators in terms of biases and mean square errors are derived up to first order of approximation. Also, the performance of the proposed class of estimators is shown theoretically and these theoretical conditions are, then, verified numerically by taking three natural populations under which the proposed class of estimators performed better than other competing estimators.

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