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Some Modified Linear Regression Type Ratio Estimators for Estimation of Population Mean Using Known Parameters of an Auxiliary Variable

J. Subramani

,

G. Kumarapandiyan

,

S. Balamurali

J. Subramani 1 G. Kumarapandiyan 1 S. Balamurali 3

  1. Department of Statistics, Ramanujan School of Mathematical Sciences, Pondicherry University, R V Nagar, Kalapet, Puducherry, India 1

  2. Department of Computer Applications, Kalasalingam University, Krishnan Koil, Srivilliputhur via, Virudhunagar – Tamilnadu, India 3


Abstract:

The present paper deals with modified linear regression type ratio estimators for estimation of population mean of the study variable when the Kurtosis, Skewness, population correlation coefficient and quartiles of the auxiliary variable are known. The bias and the mean squared error of the proposed estimators are derived and are compared with that of simple random sampling without replacement (SRSWOR) sample mean, the usual ratio estimator and the existing modified linear regression type ratio estimators. As a result, we have derived the conditions for which the proposed estimators perform better than the other existing estimators.  Further the performance of the proposed estimators with that of the existing estimators are assessed for a natural population. From the numerical study it is observed that the proposed modified ratio estimators perform better than the existing estimators. 
Contribution/ Originality

Keywords:


Reference:

  1. M. N. Murthy, Sampling theory and methods. Calcutta: Statistical Publishing Society, 1967.
  2. D. Singh and F. S. Chaudhary, Theory and analysis of sample survey designs. New Delhi: New Age International Publisher, 1986.
  3. A. L. Al-Omari, A. A. Jemain, and K. Ibrahim, "New ratio estimators of the mean using simple random sampling and ranked set sampling methods," Revista Investigación Operacional, vol. 30, pp. 97-108, 2009.
  4. C. Kadilar and H. Cingi, "Ratio estimators in simple random sampling," Applied Mathematics and Computation, vol. 151, pp. 893-902, 2004.
  5. C. Kadilar and H. Cingi, "An improvement in estimating the population mean by using the correlation coefficient," Hacettepe Journal of Mathematics and Statistics, vol. 35, pp. 103-109, 2006.
  6. Z. Yan and B. Tian, "Ratio method to the mean estimation using coefficient of skewness of auxiliary variable," ICICA 2010, Part II, CCIS, vol. 106, pp. 103–110, 2010.
  7. J. Subramani, "Generalized modified ratio estimator for estimation of finite population mean," Journal of Modern Applied Statistical Methods, vol. 12, pp. 121-155, 2013.
  8. H. Cingi and C. Kadilar, Advances in sampling theory- ratio method of estimation. Sharjah, United Arab Emirates: Bentham Science Publishers, 2009.
  9. W. G. Cochran, Sampling techniques, 3rd ed. New Delhi, India: Wiley Eastern Limited, 1977.

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Funding:

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Acknowledgement:


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