An optimal estimation approach in non-response under simple random sampling utilizing dual auxiliary variable for finite distribution function

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 <b>183.52715, 189.78448, 184.82791, 185.49885, and 223.06144</b> and when k = 3 for all the three situation of non-response is <b>223.06144, 119.32556, 165.89993, 166.29598, 112.90767 and 113.25086.</b>