This paper addresses the issue of estimating the population mean for non-response using simple random sampling. A new family of estimators is proposed for estimating the population mean with auxiliary information on the sample mean and the rank of the auxiliary variable. Bias and mean square errors of existing and proposed estimators are obtained using the first order of measurement. Theoretical comparisons are made of the performance of the proposed and existing estimators. We show that the proposed family of estimators is more efficient than existing estimators in the literature under the given constraints using these theoretical comparisons.

Auxiliary data needs to be incorporated into survey sampling in order to create a precise population parameter estimator. This study investigates improving the efficiency of these estimators, the researchers use study variable [cumulative distribution function, (CDF)] and auxiliary variable (CDF, mean and ranks) to achieve this goal in the condition of non-response. The researchers suggest two ideal families of exponential estimators to obtain an enhanced population (CDF) estimators in simple random sampling under non-response, by utilizing the data from dual auxiliary variable. The first-order approximation is used for the bias, mean squared error (MSE), and minimal mean squared error of the new and existing estimators. Using dual auxiliary information, the new families of exponential estimators turn out to be precise and efficient while estimating the distribution function, whenever non-response is contained within three Situation such as (Situation-I when non-response occurs in both study and auxiliary variables, next to it Situation-II when non-response occurs only in study variable and Situation-III when non-response occurs only in auxiliary variable). We employ a single population to assess the effectiveness and suitability of the suggested family estimators; varying values of k = 2 and 3 produce varying mean square error and percentage relative efficiency values. The suggested families of estimators have lower (MSE) and higher (PRE) values for the population which showed in tables 2–13 The percentage relative efficiency (PRE) of proposed families of estimators when k = 2 for all the three situation of non-response is 183.52715, 189.78448, 184.82791, 185.49885, and 223.06144 and when k = 3 for all the three situation of non-response is 223.06144, 119.32556, 165.89993, 166.29598, 112.90767 and 113.25086.

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.

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. The current study presents two new estimators for the distribution function of a finite population based on dual auxiliary variables. The new estimators can be used in situations where the researchers face some sort of complex data set. The mathematical equations for the bias and mean square error have been obtained for each proposed estimator. Besides, an empirical study simulation study has also been conducted to analyse the performance of estimators. It is found that the new suggested estimators of the distribution function of a finite population are more accurate than some of the existing estimators.

In this paper, a new estimator for estimating the finite population distribution function(DF) are propose using supplementary information on the DF of the auxiliary variable under simple random sampling. A comparative study is conducted to compare, theoretically and numerically, the adapted distribution function estimators of Cochran (1940), Murthy (1967), Bahl and Tuteja (1991), Rao (1991), Singh et al. (2009) and Grover and Kaur (2014) with the proposed estimators. It is found that the proposed estimators always perform better than the adapted estimators in terms of MSE and percentage relative efficiency.

In this article, we propose an improved estimator for finite population variance based on stratified sampling by using the auxiliary variable as well as the rank of the auxiliary variable. Expressions for the bias and the mean square error of the estimators are derived up to the first order of approximation. Four real data sets are used to measure the performances of estimators. Moreover, a simulation study is also conducted to observe the efficiency of the proposed variance estimator. The theoretical and numerical results show that the proposed estimator under stratified random sampling is more efficient as compared to the existing estimators.