Improved memory-type ratio estimator for population mean in stratified random sampling under linear and non-linear cost functions

This paper offers an improved memory-type ratio estimator in stratified random sampling under linear and non-linear cost functions. The issue is given as all integer non-linear programming problems (AINLPPs). The sampling properties mainly the bias and the mean squared error of the introduced estimator are derived up to the first order of approximation. The optimum value of the characterizing scalar is obtained by the Lagrange method of maxima–minima. The least value of the MSE of the suggested estimator is also obtained for this optimum value of the charactering constant. The suggested estimator is compared both theoretically and empirically with the competing estimators. Under this setup, the optimum allocation with mean square error of the suggested estimator is attained, and the estimator is compared to other comparable estimators. The AINLPP is solved using the genetic programming approach, which is applied to both actual and simulated data sets from a bivariate normal distribution.