Efficient Ratio-type Exponential Estimator for Population Variance

K.B. Panda¹ , M. Sen² , P. Das³

1. Department of Statistics, Utkal University, Bhubaneswar, India.
2. Department of Statistics, Utkal University, Bhubaneswar, India.
3. Department of Statistics, Utkal University, Bhubaneswar, India.

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.3 , pp.129-132, Jun-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i3.129132

Online published on Jun 30, 2018

Copyright © K.B. Panda, M. Sen , P. Das . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, a new exponential ratio type estimator has been proposed for estimating the population variance using auxiliary information. To the first order of approximation, i.e., to o(n-1), the expressions for the bias and the mean square error of the proposed exponential ratio-type estimator have been derived. The optimum value of the characterizing scalar, which minimizes the MSE of proposed estimator, has been obtained. With this optimum value, the expression for minimum MSE of the proposed estimator has been arrived at. The proposed estimator has been compared theoretically with sample variance, traditional ratio estimator due to Isaki [1], and exponential ratio- type estimator due to Singh et.al.[3] and it is found that, under practical conditions, the proposed estimator fares better than its competing estimators. An empirical investigation has been carried out to demonstrate the efficiency of the proposed estimator.

Key-Words / Index Term :
Auxiliary variable, single-phase sampling, mean square error, bias

References :
[1] Isaki, C.T., ‘Variance estimation using auxiliary information’, Journal of the American Statistical Association 78, pp-117-123, 1983.
[2] Panda, K.B and Sen., M (2017).Efficient Ratio-Type and Product-Type exponential estimators, Int.J.Agricult.Stat.Sci. Vol.13, No.2, pp-639-644, 2017.
[3] Singh, R., Chauhan, P., Sawan,N. & Smarandache,F.,’Improved exponential estimator for population variance using two auxiliary variables’, Italian Journal of pure ans Applied Mathematics 28,pp-101-108, 2011.
[4] Sukhatme, P.V. and Sukhatme, B.V. Sampling Theory of Surveys with Applications. Iowa State University Press, Ames., 1970.