Estimation of interquartile range in stratified sampling under non-linear cost function

Abstract

Using stratified random sampling scheme, we discuss three estimators in estimating the finite population interquartile range (IQR) by using the known values of the 1st and 3rd quartiles of the auxiliary variable. Expressions for bias and MSE are derived up to first order of approximation. We propose an allocation procedure where a non-linear cost function is considered to minimize the mean square error (MSE) of the estimators for a specified cost. We use the real data set to compare the performances of estimators under proportional allocation and proposed allocation.