Estimation of variance of the difference-cum-ratio-type exponential estimator in simple random sampling

Abstract

In this article, we have suggested a class of estimators for the estimation of the population variance of the variable of interest. The proposed estimators used some certain known information of the auxiliary variable, such as kurtosis, coefficient of variation, and the minimum and maximum values. The properties of the suggested class of estimators such as the bias and mean squared error (MSE) are obtained up to the first order of approximation. In order to check the performances of the estimators and to verify the theoretical results, we conducted a simulation study. The results of the simulation study show that the proposed class of estimators have lower MSE than other existing estimators. This holds for all simulation scenarios. In the application part, we used data from Statistical Bureau of Pakistan, and from the Textbook of Cochran, which also confirms that the suggested class of estimators is more efficient than the usual unbiased variance estimator, ratio estimator, traditional regression estimator, and other existing estimators in survey literature.