A generalized family of transformed ratio-product estimators in sample surveys

Article type: Research Article

Authors: Upadhyaya, Lakshmi N.^a | Singh, Housila P.^{b; *} | Chatterjee, S.^a | Yadav, Rohini^a

Affiliations: [a] Department of Applied Mathematics, Indian School of Mines, Dhanbad-826004, India | [b] School of Studies in Statistics, Vikram University, Ujjain-456 010, India

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: This paper addresses the problem of estimating the population mean Y¯ of the study variate Y using information on the auxiliary variable X. A family of ratio-type and product-type estimators for the population mean Y¯ of the study variable y is defined by using the suitable transformation on the study variable and the auxiliary variable. Expressions of bias and variance of the suggested class of estimators are obtained up to the first order of approximation. Several known estimators available in the literature are identified as members of the proposed family of estimators. Numerical illustration is given in the support of the present study.

Keywords: Transformed variable, ratio estimator, product estimator, study variate, auxiliary variate

DOI: 10.3233/MAS-2011-0187

Journal: Model Assisted Statistics and Applications, vol. 6, no. 2, pp. 137-150, 2011