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Sublime estimators of population variance using parameter median of study variable

Author Affiliations

  • 1Department of Statistics, Babasaheb Bhimrao Ambedkar University, Lucknow-226025, UP, India
  • 2Department of Statistics, Pondicherry University, Puducherry-605 014, India

Res. J. Mathematical & Statistical Sci., Volume 7, Issue (3), Pages 22-37, September,12 (2019)

Abstract

In the present article, we propose some enhanced ratio type and Searle type estimators for estimating parameter variance utilizing known parameter median of study variable under investigation. The study of the sampling properties of the suggested estimators are derived up to the approximation of order one. The proposed estimators are compared with the competing estimators of variance parameter of primary variable, utilizing the known auxiliary information. Numerical example depicts that the suggested estimators performs better than the competing estimators of population variance.

References

  1. Singh J. Pandey B.N. and Hirano K. (1973)., On the utilization of a known coefficient of kurtosis in the estimation procedure of variance., Ann. Inst. Stat. Math., 25, 51-55.
  2. Searls D.T. and Intarapanich P. (1990)., A note on an estimator for the variance that utilizes the kurtosis., Amer. Statistician, 44, 4, 295-296.
  3. Das A.K. and Tripathi T.P. (1978)., Use of auxiliary information in estimating the finite population variance., Sankhya, 40, 139-148.
  4. Srivastava S.K. and Jhajj H.S. (1980)., A class of estimators using auxiliary information for estimating finite population variance., Sankhya, 42, C, 87-96.
  5. Isaki C.T. (1983)., Variance estimation using auxiliary information., Journal of the American Statistical Association, 78(381), 117-123.
  6. Singh H.P., Upadhyay L.N. and Namjosh U.D. (1988)., Estimation of finite population variance., Current Science, 57(24), 1331-1334.
  7. Prasad B. and Singh H.P. (1990)., Some improved ratio-type estimators of finite population variance in sample surveys., Communications in Statistics: Theory and Methods, 19, 1127-1139.
  8. Upadhyaya L.N. and Singh H.P. (1999)., Use of transformed auxiliary variable in estimating the finite population mean., Biometrical Journal, 41(5), 627-636.
  9. Dubey V. and Kant S. (2001)., A weighted estimator of population variance using auxiliary information., Abstract, International conference on Statistical Inference and Reliability to honour Prof J. V. Despande, XXI Annual Conference of ISPS and Annual Conference of Indian Chapter of Indian Society of Bayesian Analysis, Dec 21-24, Chandigarh University.
  10. Kadilar C. and Cingi H. (2006)., Ratio estimators for the population variance in simple and stratified random sampling., Applied Mathematics and Computation, 173(2), 1047-1059.
  11. Subramani J. and Kumarapandiyan G. (2012)., Variance estimation using median of the auxiliary variable., International Journal of Probability and Statistics, 1(3), 62-66.
  12. Khan M. and Shabbir J. (2013)., A ratio-type estimator for the estimation of population variance using quartiles of an auxiliary variable., Journal of Statistics Applications and Probability, 2(3), 157-162.
  13. Yadav S.K. and Kadilar C. (2013)., Improved Exponential Type Ratio Estimator of Population Variance., Colombian Journal of Statistics, 36(1), 145-152.
  14. Yadav S.K. and Kadilar C. (2014)., A two parameter variance estimator using auxiliary information., Applied Mathematics and Computation, 226, 117-122.
  15. Yadav S.K., Kadilar C., Shabbir J. and Gupta S. (2015)., Improved Family of Estimators of Population Variance in Simple Random Sampling., Journal of Statistical Theory and Practice, 9(2), 219-226.
  16. Yadav S.K., Mishra S.S., Kumar S. and Kadilar C. (2016)., A new improved class of estimators for the population variance., Journal of Statistics Applications and Probability, 5(3), 385-392.
  17. Singh H.P. and Pal S.K. (2017)., Estimation of population variance using known coefficient of variation of an auxiliary variable in sample surveys., Journal of Statistics and Management Systems, 20(1), 91-111.
  18. Singh H.P. and Pal S.K. (2018)., An efficient new class of estimators of population variance using information on auxiliary attribute in sample surveys., Hacettepe Journal of Mathematics and Statistics, 47(1), 267-277.
  19. Bhat M.A., Mir S.A., Maqbool S., Raja T.A., Shah Ab. Rauf, Dar Z.M. and Shah Immad A. (2018)., A New Modified Approach for the Improvement of New Estimator Using Known Value of Downton's Method as Auxiliary Information for Estimating the Population Variance., Asian Journal of Agricultural Extension, Economics &Sociology, 25(3), 1-5.
  20. Upadhyaya L.N. and Singh G.N. (2001)., Chain-type estimators using transformed auxiliary variable in two-phase sampling., A.M.S.E., 38, 1-9.
  21. Gupta S. and Shabbir J. (2007)., On the use of transformed auxiliary variables in estimating population mean by using two auxiliary variables., Journal of statistical planning and inference, 137(5), 1606-1611.
  22. Singh R., Chauhan P., Sawan N. and Smarandache F. (2011)., Improved exponential estimator for population variance using two auxiliary variables., Italian Jour. of Pure and Appld. Math., 28, 103-110.
  23. Asghar A., Sanaullah A. and Hanif M. (2014)., Generalized exponential-type estimator for population variance in survey sampling., Rev. Colomb. Estad., 37(1), 211-222.
  24. Misra S., Kumari D. and Yadav D.K. (2017)., An Improved Estimator of Population Variance using known Coefficient of Variation., J. Stat. Appl. Pro. Lett., 4(1), 11-16.
  25. Milton T.K., Odhiambo R.O. and Orwa G.O. (2017)., Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling., Open Journal of Statistics, 7, 944-955.
  26. Khalil M., Ali M., Shahzad U., Hanif M. and Jamal N. (2018)., Improved Estimator of Population Variance using Measure of Dispersion of Auxiliary Variable., Orient. J. Phys. Sciences, 3, 1, 33-39.
  27. Subramani J. (2016)., A new median based ratio estimator for estimation of the finite population mean., Statistics in Transition New Series, 17(4), 591-604.
  28. Cochran W.G. (1977)., Sampling techniques., Third Edition, Wiley Eastern Limited, USA.
  29. Singh D. and Chaudhary F.S. (1986)., Theory and analysis of sample survey designs., New Age International Publisher, New Delhi.