Skip to main content
SpringerLink
Log in

A New Family of Estimators for Population Mean with Dual Use of the Auxiliary Information

  • Original Article
  • Published:
Journal of Statistical Theory and Practice Aims and scope Submit manuscript

Abstract

In this paper, a new family of estimators for the population mean is proposed using supplementary information on the mean and distribution function of the auxiliary variable. The expressions for the bias and mean square error of the proposed estimator are obtained under first order of approximation. The proposed estimator is compared with the existing estimators of the population mean (theoretically and numerically). A numerical study is conducted to examine the efficiencies of the existing and proposed estimators. It turns out that the proposed estimator is always more efficient than its existing counterparts in terms of percentage relative efficiency.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bahl S, Tuteja RK (1991) Ratio and product type exponential estimators. J Inf Optim Sci 12(1):159–164

    MathSciNet  MATH  Google Scholar 

  2. Bedi PK (1996) Efficient utilization of auxiliary information at estimation stage. Biomet J 38(8):973–976

    Article  Google Scholar 

  3. Cochran WG (1940) The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. J Agric Sci 30(2):262–275

    Article  Google Scholar 

  4. Grover LK, Kaur P (2011) An improved estimator of the finite population mean in simple random sampling. Model Assist Stat Appl 6(1):47–55

    MATH  Google Scholar 

  5. Grover LK, Kaur P (2014) A generalized class of ratio type exponential estimators of population mean under linear transformation of auxiliary variable. Commun Stat Simul Comput 43(7):1552–1574

    Article  MathSciNet  Google Scholar 

  6. Gujarati DN (2009) Basic econometrics. Tata McGraw-Hill Education, New York

    Google Scholar 

  7. Gupta S, Shabbir J (2008) On improvement in estimating the population mean in simple random sampling. J Appl Stat 35(5):559–566

    Article  MathSciNet  Google Scholar 

  8. Haq A, Khan M, Hussain Z (2017) A new estimator of finite population mean based on the dual use of the auxiliary information. Commun Stat Theory Methods 46(9):4425–4436

    Article  MathSciNet  Google Scholar 

  9. Kadilar C, Cingi H (2006) New ratio estimators using correlation coefficient. InterStat 4:1–11

    MATH  Google Scholar 

  10. Murthy MN (1964) Product method of estimation. Sankhyā Indian J Stat Ser A 26(1):69–74

    MathSciNet  MATH  Google Scholar 

  11. Murthy MN (1967) Sampling theory and methods. Statistical Publishing Society, London

    MATH  Google Scholar 

  12. Rao TJ (1991) On certail methods of improving ration and regression estimators. Commun Stat Theory Methods 20(10):3325–3340

    Article  Google Scholar 

  13. Shabbir J, Gupta S (2005) Improved ratio estimators in stratified sampling. Am J Math Manag Sci 25(3–4):293–311

    MathSciNet  MATH  Google Scholar 

  14. Singh H, Tailor R (2003) Use of known correlation coefficient in estimating the finite population mean. Stat Transit 6(4):555–560

    Google Scholar 

  15. Singh R, Chauhan P, Sawan N, Smarandache F (2009) Improvement in estimating the population mean using exponential estimator in simple random sampling. Int J Stat Econ 3(A09):13–18

    MathSciNet  Google Scholar 

  16. Singh S (2003) Advanced sampling theory with applications: how michael ‘selected’ amy, vol 2. Springer, Berlin, p 2

    Book  Google Scholar 

  17. Sisodia B, Dwivedi V (1981) Modified ratio estimator using coefficient of variation of auxiliary variable. J Indian Soc Agric Stat 33:13–18

    Google Scholar 

  18. Srivastava S, Jhajj H (1983) A class of estimators of the population mean using multiauxiliary information. Calcutta Stat Assoc Bull 32(1–2):47–56

    Article  Google Scholar 

  19. Upadhyaya LN, Singh HP (1999) Use of transformed auxiliary variable in estimating the finite population mean. Biomet J 41(5):627–636

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the anonymous reviewers for providing useful comments.

Author information

Authors and Affiliations

  1. Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan

    Ishfaq Hussain & Abdul Haq

Authors
  1. Ishfaq Hussain
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Abdul Haq
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Abdul Haq.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hussain, I., Haq, A. A New Family of Estimators for Population Mean with Dual Use of the Auxiliary Information. J Stat Theory Pract 13, 23 (2019). https://doi.org/10.1007/s42519-018-0023-6

Download citation

  • Published:

  • DOI: https://doi.org/10.1007/s42519-018-0023-6

Keywords

Search

Navigation