In this article, our main aim is to suggest enhanced families of estimators for estimating the population distribution function (DF) using twofold auxiliary evidence within the framework of simple random sampling. Numerical analysis is performed on four different actual data sets. The precision of the estimators is further investigated exhausting a simulation study. As equated with existing estimators, the suggested families of estimators have minimum mean square error (MSE) and higher percentage relative efficiency (PRE). The succeeding recommended family of estimators outperforms the first family of estimators across all data sets. These are positive indicators of its performance. The theoretical result shows that the recommended family of estimators performs better than the existing estimators. The extent of improvement in efficiency is noteworthy, indicating the superiority of the suggested estimators in terms of minimum MSE.

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.

The article introduces a novel class of estimators designed for estimating finite population proportions. These estimators utilize dual auxiliary attributes and are applicable under simple random sampling. The proposed class of estimators includes various members with distinct characteristics. The article provides numerical terminologies for the bias and MSE of the estimators, acquire up to first order of approximation. Four actual data sets are used. Additionally, a simulation study is accompanied to perceive the presentations of estimators. The MSE criterion is used to assess how well the proposed estimator performed as likened to the preliminary estimators. The simulation analysis revealed that, in contrast to other examined estimators, the suggested class of estimators provided better results. The empirical investigation offers evidence to substantiate the findings of the argument. Theoretical research also displays that the suggested class of estimators outperforms its competitors.

In this study, we apply a predictive approach to the problem of finding new estimators for the estimation of finite population mean using auxiliary variable under probability proportional to size (PPS) sampling. This work is deemed novel due to the fact that, as far as we are aware, no one has before investigated the predictive approach to estimating the finite population mean under probability proportional to size sampling. The expressions for the bias and mean square error (MSE) are derived up to the first order. In order to verify the theoretical results, numerical and simulation investigations are conducted respectively. Based on the numerical result, it is shown that the suggested estimator performs well in terms of minimum MSE and higher percentage relative efficiency (PRE). The conditions under which the suggested estimator is more efficient than the other estimators are described numerically.

This article aims to suggest a new generalized class of estimators based on probability proportional to size sampling using two auxiliary variables. The numerical expressions for the bias and mean squared error (MSE) are derived up to the first order of approximation. Four actual data sets are used to examine the performances of a new improved generalized class of estimators. From the results of real data sets, it is examined that the suggested estimator gives the minimum MSE and the percentage relative efficiency is higher than all existing estimators, which shows the importance of the new generalized class of estimators. To check the strength and generalizability of our proposed class of estimators, a simulation study is also accompanied. The consequence of the simulation study shows the worth of newly found proposed class estimators. Overall, we get to the conclusion that the proposed estimator outperforms as compared to all other estimators taken into account in this study.