Advertisement

Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 285–302 | Cite as

Improved Ratio and Product Exponential Type Estimators

  • Lakshmi N. Upadhyaya
  • Housila P. Singh
  • S. Chatterjee
  • Rohini Yadav
Article

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.

Key-word

Study variable Auxiliary variable Bias Mean squared error 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bahl, S., Tuteja, R.K., 1991. Ratio and product type exponential estimator. Information and Optimization Sciences, 12, 159–163.MathSciNetCrossRefGoogle Scholar
  2. 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.CrossRefGoogle Scholar
  3. Cochran, W.G., 1963. Sampling Techniques, 3rd Edition. Wiley, New YorkzbMATHGoogle Scholar
  4. Das, A.K., 1988. Contributions to the theory of sampling strategies based on auxiliary information. Ph.D. Thesis, Bidhan Chandra Krishi Vishwavidyalaya, Nadia.Google Scholar
  5. Dobson, A.J., 1990. An Introduction to Generalized Linear Models, 1st Edition. Chapman and Hall, New York.CrossRefGoogle Scholar
  6. Fisher, R.A., 1936. The use of multiple measurements in taxonomic problems. Ann. Eugen., 7, 179–188.CrossRefGoogle Scholar
  7. Murthy, M.N., 1964. Product method of estimation. Sankhya, 26, 69–74.MathSciNetzbMATHGoogle Scholar
  8. Murthy, M.N., 1967. Sampling Theory and Methods. Calcutta Statistical Publishing Society, Kolkatta, India.zbMATHGoogle Scholar
  9. Rao, T.J., 1983. A new class of unbiased product estimators. Technical report, Indian Statistical Institute, Calcutta.Google Scholar
  10. Reddy, V.N., 1973. On ratio and product methods of estimation. Sankhya, Ser. B, 35(3), 307–316.MathSciNetGoogle Scholar
  11. Reddy, V.N., 1974. On a transformed ratio method of estimation. Sankhya, Ser. C, 36, 59–70.zbMATHGoogle Scholar
  12. Robson, D.S., 1957. Applications of multivariate polykays to the theory of unbiased ratio type estimation. Jour. Amer. Statst. Assoc., 52, 511–522.MathSciNetCrossRefGoogle Scholar
  13. Sahai, A., Ray, S.K., 1980. An efficient estimator using auxiliary information. Metrika, 27, 271–275.MathSciNetCrossRefGoogle Scholar
  14. 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.MathSciNetCrossRefGoogle Scholar
  15. 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.MathSciNetCrossRefGoogle Scholar
  16. 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.MathSciNetCrossRefGoogle Scholar
  17. Srivenkataramana, T., Tracy, D.S., 1980. An alternative to ratio method in sample surveys. Ann. Inst. Statist. Math., 32, 111–120.MathSciNetCrossRefGoogle Scholar
  18. Steel, R.G.D., Torrie, J.H., 1960. Principles and Procedures of Statistics. McGraw-Hill, New York.zbMATHGoogle Scholar
  19. Sukhatme, P.V., Sukhatme, B.V., 1970. Sampling Theory of Surveys with Applications. Asia Publishing House, India.zbMATHGoogle Scholar

Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  • Lakshmi N. Upadhyaya
    • 1
  • Housila P. Singh
    • 2
  • S. Chatterjee
    • 1
  • Rohini Yadav
    • 1
  1. 1.Department of Applied MathematicsIndian School of MinesDhanbadIndia
  2. 2.School of Studies in StatisticsVikram UniversityUjjainIndia

Personalised recommendations