Advertisement

Journal of Statistical Theory and Practice

, Volume 9, Issue 2, pp 219–226 | Cite as

Improved Family of Estimators of Population Variance in Simple Random Sampling

  • Subhash Kumar Yadav
  • Cem Kadilar
  • Javid Shabbir
  • Sat Gupta
Article

Abstract

In this article, we suggest a general procedure for estimating the population variance through a class of estimators. The bias and mean square error (MSE) of the proposed class of estimators are obtained to the first degree of approximation. The proposed class of estimators is more efficient than many other estimators, such as the usual variance estimator, ratio estimator, the Bahal and Tuteja (1991) exponential estimator, the traditional regression estimator, the Rao (1991) estimator, the Upadhyaya and Singh (1999) estimator, and the Kadilar and Cingi (2006) estimators. Four data sets are used for numerical comparison.

Keywords

Auxiliary variable Bias MSE Efficiency 

AMS Subject Classification

62D05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bahl, S., and R. K. Tuteja. 1991. Ratio and product type exponential estimator. Information Optimiz. Sci., 12, 159–163.MathSciNetCrossRefGoogle Scholar
  2. Isaki, C. T. 1983. Variance estimation using auxiliary information. J. Am. Stat. Assoc., 78, 117–123.MathSciNetCrossRefGoogle Scholar
  3. Kadilar, C., and H. Cingi. 2006. Ratio estimators for the population variance in simple and stratified sampling. App. Math. Computation, 173, 1047–1059.MathSciNetCrossRefGoogle Scholar
  4. Murthy, M. N. 1967. Sampling theory and methods. Calcutta, India: Statistical Publishing Society.MATHGoogle Scholar
  5. Rao, T. J. 1991. On certain methods of improving ratio and regression estimators. Commun. Stat. Theory Methods, 20, 3325–3340.MathSciNetCrossRefGoogle Scholar
  6. Singh, R., and N. S. Mangat. 1996. Elements of survey sampling. Dordrecht, The Netherlands: Kluwer Academic.CrossRefGoogle Scholar
  7. Singh, R., M. Kumar, and M. K. Chaudhary. 2011. Improved family of estimators of population mean in simple random sampling. World Appl. Sci. J., 13(10), 2131–2136.Google Scholar
  8. Upadhyaya, L. N., and H. P. Singh. 1999. An estimator for population variance that utilizes the kurtosis of an auxiliary variable in sample surveys. Vikram Math. J., 19, 14–17.MATHGoogle Scholar

Copyright information

© Grace Scientific Publishing 2015

Authors and Affiliations

  • Subhash Kumar Yadav
    • 1
  • Cem Kadilar
    • 2
  • Javid Shabbir
    • 3
  • Sat Gupta
    • 4
  1. 1.Department of Mathematics and Statistics (A Centre of Excellence)Dr. RML Avadh UniversityFaizabad, Uttar PradeshIndia
  2. 2.Department of StatisticsHacettepe UniversityAnkaraTurkey
  3. 3.Department of StatisticsQuaid-i-Azam UniversityIslamabadPakistan
  4. 4.Department of Mathematics and StatisticsUniversity of North Carolina at GreensboroGreensboroUSA

Personalised recommendations