In this study, we propose a new improved estimator of population mean for the sensitive variable in the presence of measurement error under simple and stratified random sampling. This estimator accounts the auxiliary information as well as the ranks of the auxiliary variable. From theoretical and numerical studies it is shown that a new improved estimator performs better than the existing estimators under study.

In the present paper we propose an improved class of estimators in the presence of measurement error and non-response under stratified random sampling for estimating the finite population mean. The theoretical and numerical studies reveal that the proposed class of estimators performs better than other existing estimators.

The main objective of the current study is to suggest an enhanced family of log ratio-exponential type estimators for population distribution function (DF) using auxiliary information under stratified random sampling. Putting different choices in our suggested generalized class of estimators, we found some Specific estimators. The bias and MSE expressions of the estimators have been approximated up to the first order. By using the actual and simulated data sets, we measured the performance of estimators. Based on the results, the suggested estimators for DF show better performance as compared to the preliminary estimators considered here. The suggested estimators have a advanced efficiency than the other estimators examined with the estimators ${\widehat{\stackrel{‾}{F}}}_{logPR\left(st\right)}^2$, and ${\widehat{\stackrel{‾}{F}}}_{logPR\left(st\right)}^4$ for both the actual and simulated data sets. The magnitude of the improvement in efficiency is noteworthy, indicating the superiority of the proposed estimators in terms of MSE.

In this paper, a general class of estimators is proposed for estimating the finite population mean for sensitive variable, in the presence of measurement error and non-response in simple random sampling. Expressions for bias and mean square error up to first order of approximation, are derived. Impact of measurement errors is examined using real data sets, including the survey conducted at Quaid-i-Azam University, Islamabad. Simulated data sets are also used to observe the performance of the proposed estimators in comparison to some other estimators. We obtain the empirical bias and MSE values for the proposed and the competing estimators.

In survey sampling, information on auxiliary variables related to the main variable is often available in many practical problems. Since the mid-twentieth century, researchers have taken a keen interest in the use of auxiliary information, due to its usefulness in estimation methods. In this article, our main objective is to discover the problem associated with estimation of the finite population distribution function, using the known auxiliary variable, which occurs as the sample distribution function and the rank of the auxiliary variable. A new family of the finite population distribution function estimators is proposed in the stratified sampling scheme. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator, along with the eciency conditions. Besides theoretical eciency comparison, an empirical study has also been conducted to analyze the performance of estimators. A simulation study is also performed to observe the efficiency of the proposed estimators. The implementation of the proposed sampling scheme is illustrated by a practical example.