Efficient Estimators of Population Variance Using Known Population Mode & Variance of Auxiliary Variable

Harinder Kaur, M. K. Sharma

Abstract: In this paper, using known information of population mode (M_x) along with population variance (S_x^2) of the auxiliary variable x, we have proposed the ratio-type and product-type estimators of population variance (S_y^2) of the main variable y. Also we have proposed the class of estimators of S_y^2 whose proposed estimators are the members. Up to terms of order n^(-1), expressions for biases, MSEs and minimum MSEs are obtained and compared with each other. Theoretical results are supported by the empirical study by taking five populations from the literature.

Keywords: Correlation coefficient, Coefficient of kurtosis, Coefficient of skewness, Population variance, Population mode, Product-type estimator, Ratio-type estimator, Regularity conditions, Taylor series