Efficient Modified Estimators for the Population Mean Using Auxiliary Variables
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Published
Sep 9, 2022
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Abstract
This paper presents three modified estimators to estimate the population mean by utilizing information on auxiliary variables under simple random sampling without replacement (SRSWOR). Motivation for the proposed estimators is based on Yadav et al. (2019). Furthermore, the expressions for bias and mean squared error (MSE) of proposed estimators were obtained and compared with other relevant existing estimators through theoretical and empirical studies. It is shown that the proposed estimators perform better than other estimators.
Keywords: Modified estimators, Auxiliary variable, Bias, MSE
References
Al-Omari, A. I., Jemain, A. A., & Ibrahim, K. (2009). New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Investigación Operacional, 30(2), 97-108.
Cochran, W. G. (1940). The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce. Journal of Agricultural Science, 30, 262-275.
Jeelani, M.I., Maqbool, S., & Mir, S. A. (2013). Modified ratio estimators of population mean using linear combination of co-efficient of skewness and quartile deviation. International Journal of Modern Mathematical Sciences, 6(3), 174-183.
Jerajuddin, M., & Kishun, J. (2016). Modified ratio estimators for population mean using size of the sample, selected from population. International Journal of Scientific Research in Science, Engineering and Technology, 2(2), 10-16.
Kadilar, C., & Cingi, H. (2004). Ratio Estimators in Simple Random Sampling. Applied Mathematics and Computation, 151, 893-902.
Kadilar, C., & Cingi, H. (2006). An improvement in estimating the population mean by using the correlation coefficient. Hacettepe Journal of Mathematics and Statistics, 35(1), 103-109.
Khoshnevisan, M., Singh, R., Chauhan, P., Sawan, N., & Smarandache, F. (2007). A general family of estimators for estimating population mean using known value of some population parameter(s). Far East Journal of Theoretical Statistics, 22, 181-191.
Murthy, M. N. (1964). Product method of estimation. Sankhya, 26A, 69-74.
Pandey, B.N., & Dubey, V. (1988). Modified product estimator using coefficient of variation of auxiliary variate. Assam Statistical Review, 2(2), 64-66.
Ray, S.K. & Singh, R.K. (1981). Difference-cum-ratio type estimators. Journal of Indian Statistical Association, 19, 147-151.
Robson, D. S. (1957). Application of multivariate polykays to the theory of unbiased ratio-type estimation. Journal of the American Statistical Association, 52, 511-522.
Singh, G. N. (2003). On the improvement of product method of estimation in sample surveys. Journal of the Indian Society of Agricultural Statistics, 56(3), 267-275.
Singh, H.P., & Tailor, R.(2003). Use of known correlation coefficient in estimating the finite
population mean. Statistics in Transition, 6, 555-560.
Singh H. P., Tailor, R., & Kakaran, M. S. (2004). An estimator of population mean using power transformation. Journal of Indian Society of Agricultural Statistics, 58(2), 223-230.
Singh H.P., & Tailor, R. (2005). Estimation of finite population mean using known correlation coefficient between auxiliary characters. Statistica, 65(4), 407-418.
Singh H. P., Tailor, R., & Tailor, R. (2012). Estimation of finite population mean in two-phase sampling with known coefficient of variation of an auxiliary character. Statistica, 72(1), 111-126.
Singh H. P., Upadhyaya, L. N., & Tailor, R. (2009). Ratio-cum-product type exponential estimator. Statistica, 69(4), 299-310.
Sisodia, B. V. S., & Dwivedi, V. K. (1981). A modified ratio estimator using coefficient of variation of auxiliary variable. Journal of Indian Society of Agricultural Statistics, 33, 13-18.
Subramani, J., & Kumarapandiyan, G. (2012). Estimation of population mean using co-efficient of variation and median of an auxiliary variable. International Journal of Probability and Statistics, 1(4), 111–118.
Upadhyaya, L. N., & Singh, H.P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical Journal, 41(5), 627-636.
Yadav, S. K., Dixit, M.K., Dungana, H.N., & Mishra, S.S. (2019). Improved estimators for estimating average yield using auxiliary variable. International Journal of Mathematical Engineering and Management Sciences, 4, 1228-1238.
Yan, Z., & Tian, B. (2010). Ratio method to the mean estimation using coefficient of skewness of auxiliary variable. Information Computing and Applications, 106, 103-110.
Cochran, W. G. (1940). The estimation of the yields of the cereal experiments by sampling for the ratio of grain to total produce. Journal of Agricultural Science, 30, 262-275.
Jeelani, M.I., Maqbool, S., & Mir, S. A. (2013). Modified ratio estimators of population mean using linear combination of co-efficient of skewness and quartile deviation. International Journal of Modern Mathematical Sciences, 6(3), 174-183.
Jerajuddin, M., & Kishun, J. (2016). Modified ratio estimators for population mean using size of the sample, selected from population. International Journal of Scientific Research in Science, Engineering and Technology, 2(2), 10-16.
Kadilar, C., & Cingi, H. (2004). Ratio Estimators in Simple Random Sampling. Applied Mathematics and Computation, 151, 893-902.
Kadilar, C., & Cingi, H. (2006). An improvement in estimating the population mean by using the correlation coefficient. Hacettepe Journal of Mathematics and Statistics, 35(1), 103-109.
Khoshnevisan, M., Singh, R., Chauhan, P., Sawan, N., & Smarandache, F. (2007). A general family of estimators for estimating population mean using known value of some population parameter(s). Far East Journal of Theoretical Statistics, 22, 181-191.
Murthy, M. N. (1964). Product method of estimation. Sankhya, 26A, 69-74.
Pandey, B.N., & Dubey, V. (1988). Modified product estimator using coefficient of variation of auxiliary variate. Assam Statistical Review, 2(2), 64-66.
Ray, S.K. & Singh, R.K. (1981). Difference-cum-ratio type estimators. Journal of Indian Statistical Association, 19, 147-151.
Robson, D. S. (1957). Application of multivariate polykays to the theory of unbiased ratio-type estimation. Journal of the American Statistical Association, 52, 511-522.
Singh, G. N. (2003). On the improvement of product method of estimation in sample surveys. Journal of the Indian Society of Agricultural Statistics, 56(3), 267-275.
Singh, H.P., & Tailor, R.(2003). Use of known correlation coefficient in estimating the finite
population mean. Statistics in Transition, 6, 555-560.
Singh H. P., Tailor, R., & Kakaran, M. S. (2004). An estimator of population mean using power transformation. Journal of Indian Society of Agricultural Statistics, 58(2), 223-230.
Singh H.P., & Tailor, R. (2005). Estimation of finite population mean using known correlation coefficient between auxiliary characters. Statistica, 65(4), 407-418.
Singh H. P., Tailor, R., & Tailor, R. (2012). Estimation of finite population mean in two-phase sampling with known coefficient of variation of an auxiliary character. Statistica, 72(1), 111-126.
Singh H. P., Upadhyaya, L. N., & Tailor, R. (2009). Ratio-cum-product type exponential estimator. Statistica, 69(4), 299-310.
Sisodia, B. V. S., & Dwivedi, V. K. (1981). A modified ratio estimator using coefficient of variation of auxiliary variable. Journal of Indian Society of Agricultural Statistics, 33, 13-18.
Subramani, J., & Kumarapandiyan, G. (2012). Estimation of population mean using co-efficient of variation and median of an auxiliary variable. International Journal of Probability and Statistics, 1(4), 111–118.
Upadhyaya, L. N., & Singh, H.P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical Journal, 41(5), 627-636.
Yadav, S. K., Dixit, M.K., Dungana, H.N., & Mishra, S.S. (2019). Improved estimators for estimating average yield using auxiliary variable. International Journal of Mathematical Engineering and Management Sciences, 4, 1228-1238.
Yan, Z., & Tian, B. (2010). Ratio method to the mean estimation using coefficient of skewness of auxiliary variable. Information Computing and Applications, 106, 103-110.
Section
Research Articles
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How to Cite
DANSAWAD, Napattchan.
Efficient Modified Estimators for the Population Mean Using Auxiliary Variables.
Naresuan University Journal: Science and Technology (NUJST), [S.l.], v. 30, n. 4, p. 84-93, sep. 2022.
ISSN 2539-553X.
Available at: <https://www.journal.nu.ac.th/NUJST/article/view/Vol-30-No-4-2022-84-93>. Date accessed: 19 apr. 2024.
doi: https://doi.org/10.14456/nujst.2022.38.