Abstract
This paper addresses the problem of estimating the population mean using auxiliary information. Improved versions of Bahl and Tuteja (1991) ratio and product exponential type estimators have been proposed and their properties studied under large sample approximation. It has been shown that the proposed ratio and product exponential type estimators are more efficient than those considered by Bahl and Tuteja (1991) estimators, conventional ratio and product estimators and the usual unbiased estimator under some realistic conditions. An empirical study has been carried out to judge the merits of the suggested estimators over others. Theoretical and empirical results are sound and quite illuminating compared to other estimators.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bahl, S., Tuteja, R.K., 1991. Ratio and product type exponential estimator. Information and Optimization Sciences, 12, 159–163.
Cochran, W.G., 1940. The estimation of the yields of cereal experiments by sampling for the ratio gain to total produce. Jour. Agri. Soc, 30, 262–275.
Cochran, W.G., 1963. Sampling Techniques, 3rd Edition. Wiley, New York
Das, A.K., 1988. Contributions to the theory of sampling strategies based on auxiliary information. Ph.D. Thesis, Bidhan Chandra Krishi Vishwavidyalaya, Nadia.
Dobson, A.J., 1990. An Introduction to Generalized Linear Models, 1st Edition. Chapman and Hall, New York.
Fisher, R.A., 1936. The use of multiple measurements in taxonomic problems. Ann. Eugen., 7, 179–188.
Murthy, M.N., 1964. Product method of estimation. Sankhya, 26, 69–74.
Murthy, M.N., 1967. Sampling Theory and Methods. Calcutta Statistical Publishing Society, Kolkatta, India.
Rao, T.J., 1983. A new class of unbiased product estimators. Technical report, Indian Statistical Institute, Calcutta.
Reddy, V.N., 1973. On ratio and product methods of estimation. Sankhya, Ser. B, 35(3), 307–316.
Reddy, V.N., 1974. On a transformed ratio method of estimation. Sankhya, Ser. C, 36, 59–70.
Robson, D.S., 1957. Applications of multivariate polykays to the theory of unbiased ratio type estimation. Jour. Amer. Statst. Assoc., 52, 511–522.
Sahai, A., Ray, S.K., 1980. An efficient estimator using auxiliary information. Metrika, 27, 271–275.
Singh, H.P., Karpe, N., 2010. Estimation of mean, ratio and product using auxiliary information in the presence of measurement errors in sample surveys. Jour. Statist. Theo. Pract., 4(1), 111–136.
Singh, H.P., Kumar, S., 2008. A general family of estimators of finite population ratio, product and mean using two phase sampling scheme in the presence of non-response. Jour. Statist. Theo. Pract., 2(4), 677–692.
Singh, H.P., Vishwakarma, G.K., 2008. Some families of estimators of variance of stratified random sample mean using auxiliary information. Jour. Statist. Theo. Pract., 2(1), 21–43.
Srivenkataramana, T., Tracy, D.S., 1980. An alternative to ratio method in sample surveys. Ann. Inst. Statist. Math., 32, 111–120.
Steel, R.G.D., Torrie, J.H., 1960. Principles and Procedures of Statistics. McGraw-Hill, New York.
Sukhatme, P.V., Sukhatme, B.V., 1970. Sampling Theory of Surveys with Applications. Asia Publishing House, India.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Upadhyaya, L.N., Singh, H.P., Chatterjee, S. et al. Improved Ratio and Product Exponential Type Estimators. J Stat Theory Pract 5, 285–302 (2011). https://doi.org/10.1080/15598608.2011.10412029
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1080/15598608.2011.10412029