On the optimal search for efficient estimators of population mean in simple random sampling in the presence of an auxiliary variable

Year 2018, Volume: 47 Issue: 4, 963 - 982, 01.08.2018

Ekaette İnyang Enang Emmanuel John Ekpenyong

Abstract

This study proposes some ratio estimators of the population mean under simple random sampling schemes, in order to tackle the problem of
low efficiencies of some existing estimators. An improved exponential ratio estimator of the population mean under simple random sampling scheme and its bias and mean square error have been derived. Further propositions of a generalized form of the exponential ratio estimator of
the population mean under simple random sampling scheme has also been made. The Bias and Mean Square Errors of these class of estimators have also been obtained. It is observed that some existing estimators are members of this class of estimators of population mean.
Analytical and numerical results indicate that, the Asymptotic Optimal Estimator (AOE) of these proposed estimators of population mean using single auxiliary variable have been found to exhibit greater gains in efficiencies than the classical regression estimators and other existing
estimators in simple random sampling scheme.

Keywords

Ratio estimators, Efficiency, Asymptotic Optimal Estimators(AOE), generalized exponential estimators, population mean

References

• Bahl, S. and Tuteja, R. K. Ratio and product type exponential estimator, Journal of Infor- mation and Optimization Sciences 12 (1), 159-164, 1991.
• Chami, P.S. and Singh, B. and Thomas, D. A two-parameter ratio-product-ratio esti- mator using auxiliary information, ISRN probability and Statistics. Article ID 103860. doi:10.5402/2012/103860.
• Cochran, W. G. Sampling Techniques, 3rd Edition, John Wiley and Sons, New York, 1977.
• Das, A. Contributions to the Theory of Samppling Strategies based on auxiliary Information, Ph.D Thesis, Bidhan Chandra Krishi Viswavidyalay, Nadia, West Bengal, India, 1988.
• Ekpenyong, E.J. and Enang, E.I. Efficient exponential estimator for estimating the popu- lation mean in simple random sampling, Hacettepe Journal of Mathematics and Statistics 40 (3), 689-705, 2015.
• Gupta, S. and Shabbir, J. On the improvement in estimating the population mean in simple random sampling, Journal of Applied Sciences, 35 (5), 559-566, 2008.
• Grover, L. K. and Kaur, P. An improved estimator of the finite population mean in simple random sampling, Model Assisted Statistics and Applications, 6 (1), 47-55, 2011.
• Grover, L. K. and Kaur, P. A generalized class of ratio type exponential estimators of popu- lation mean under linear transformation of auxiliary variables, Communication in Statistics - Simulation and Computation, 43 (7), 1552 - 1574, 2014.
• Jeelani, M. I., Maqbool, S. and Mir S. A. Modified Ratio Estimators of population mean using linear combination of coefficient of skewness and quartile deviation, International Journal of Modern Mathematics Science, 6 (3), 174-183, 2013.
• Jitthavech, J. and Lorchirachoon, V. Estimators in simple random sampling: Searls ap- proach, Songklanakarin Journal of Science and Technology, 35 (6), 749-760, 2013.
• Kadilar, C. and Cingi, H. A study on the chain ratio-type estimator, Hacettepe Journal of Mathematics and Computation, 32, 105 - 108, 2003.
• Kadilar, C. and Cingi H. Ratio estimators in simple random sampling, Applied Mathematics and Computation, 151, 893-902, 2004.
• Kadilar, C. and Cingi, H. A new estimator using two auxiliary variables, Applied Mathe- matics and Computation, 151, 893-902, 2005.
• Kadilar, C. and Cingi, H. An improvement in estimating the population mean by using the correlation coefficient, hacettepe Journal of Mathematics and Statistics, 35 (1), 103 - 109, 2006.
• Kadilar, C. and Cingi, H. New Ratio Estimators Using Correlation Coefficient, http://interstat.statjournals.net/YEAR/2006/articles/0603004.pdf, 2006.
• Kadilar, C. and Cingi, H. Improvement in variance estimation using auxiliary information, Hacettepe Journal of Mathematics and Statistics, 35 (1), 111 - 115, 2006.
• Kadilar, C. and Cingi, H. Improvement in estimating the population mean in simple random sampling, Applied Mathematics Letter, 19 (1), 75 - 79, 2006.
• Khan, H. and Siddiqi, A.F. A new class of generalized exponential ratio and product type estimators for population mean using variance of an auxiliary variable, Journal of Statistics, 21, 206-214, 2014.
• Koyuncu, N. and Cingi, H. Efficient estimators for population mean, Hacettepe Journal of Mathematics and Statistics, 38 (28), 217 - 225, 2009.
• Khoshnevisan, M., Singh, R. and Chauhan, P., Sawan, N. and Smarandache, F. A general family of estimators for estimating population mean using known value of some population parameter(s), Far East Journal of Theoretical Statistics, 22 (2), 272-276, 2007.
• Kurma, M., Singh, R., Singh, A.K. and Smarandache, F. Some ratio type estimators under measurement error, World Applied Sciences Journal, 14 (2), 272 - 276, 2011.
• Murthy, M.N. Product method of estimation, Sankhya: Indian J. Stat. Ser. A, 26, 69 - 74, 1964.
• Murthy, M.N. Sampling Theory and Methods, Statistical Publishing Society, Calcutta, India, 1967.
• Rao, T. On certain methods of improving ratio and regression estimators, Communication in Statistics-Theory and Methods, 20 (10), 3325-3340, 1991.
• Sanaullah, A. and Khan, H. and Ali, H. A. and Singh, R. Improved exponential ratio-type estimators in survey sampling, Journal of Reliability and Statistical Studies, 5(2), 119-132, 2012.
• Sen, A.R. Estimation of the population mean when the coefficient of variation is known: Estimation of the population mean, Communications in Statistics-Theory and Methods, 7(7), 657-672, 1978.
• Scheaer, R.L. and Mendenhall, W. and Ott, L. Elementary survey sampling, 4th edn. PWS, KENT Publishing Company, Boston, Massachusetts, USA, 1990.
• Searls, D. T. The utilization of a known coefficient of variation in the estimation procedure, Journal of the American Statistical Association, 59(308), 1225-1226, 1964.
• Sharma, B. and Tailor, R. A new ratio-cum-dual to ratio estimator of finite population mean in simple random sampling, Global Journal of Science Frontier Research, 10(1), 27-31, 2010.
• Sharma, B. and Tailor, R. An Alternative Ratio-Cum-Product Estimator of Finite Popula- tion Mean Using Coefficient of Kurtosis of Two Auxiliary Variates in Two-Phase Sampling, Pakistan Journal of Statistics and Operation Research, 10(3), 257-266, 2014.
• Shabbir, J. and Haq, A. and Gupta, S. A new difference-cum-exponential type estimator of finite population mean in simple random sampling, Revista Colombiana de Estadfstica, 37(1), 199-211, 2014.
• Singh, R. and Chauhan, P. and Sawan, N. and Smarandache, F. Improvement in estimating the population mean using exponential estimator in simple random sampling, Bulletin of Statistics and Economics, 3(9), 13-18, 2009.
• Singh, H. P. and Espejo, M. R. On linear regression and ratioproduct estimation of a finite population mean, Journal of the Royal Statistical Society: Series D (The Statistician), 52(1), 59-67, 2003.
• Singh, R. and Kumar, M. and Smarandache, F. Almost unbiased estimator for estimating population mean using known value of some population parameter (s), Pakistan Journal of Statistics and Operation Research, 6(2), 63-76, 2008.
• Singh, H. P. and Rathour, A. and Solanki, R. S. An improved dual to chain ratio type estimator for the population mean, Journal of Statistics, 1(3), 1-6, 2013.
• Singh, H.P. and Tailor, R. Use of known correlation coefficient in estimating the finite population mean, Statistics in Transition, 6(4), 555-560, 2003.
• Singh, H. P. and Tailor, R. Estimation of finite population mean with known coefficient of variation of an auxiliary character, Statistica, 65(3), 301-313, 2005.
• Singh, H. P. and Tailor, R. Estimation of finite population mean using known correlation coefficient between auxiliary characters, Statistica, 65(4), 407-418, 2005.
• Singh, H. P. and Tailor, R. and Singh, S. and Kim, J. M. A modified estimator of population mean using power transformation, Statistical papers, 49(1), 37-58, 22008.
• Singh, H. P. and Tailor, R. and Kakran, M. S. A modified ratio estimator of population mean, Jour. Ind. Soc. Agri. Stat, 33(1), 13-18, 2004.
• Singh, G. N. and Upadhyaya, L. N. A class of modified chain type estimators using two auxiliary variables in two-phase sampling, Metron, 53(3), 117-125, 1995.
• Singh, H. P. and Solanki, R. S. An alternative procedure for estimating the population mean in simple random sampling, Pakistan Journal of Statistics and Operation Research, 8(2), 213-232, 2012.
• Singh, R. and Kumar, M. and Chaudhary, M. K. Improved family of estimators of population mean in simple random sampling, World Applied Sciences Journal, 13(10), 2131-2136, 2011.
• Solanki, R. S. and Singh, H. P. and Rathour, A. An alternative estimator for estimating the finite population mean using auxiliary information in sample surveys, ISRN Probability and Statistics, Article ID 657682, doi:10.5402/2012/657682, 2012.
• Sosidia, B. V. and Dwivedi, V. K. A modified ratio estimator using coefficient of variation of auxiliary variable, Jour, Ind. Soc. Agri. Stat., 33(1), 13-18, 1981.
• Srivnstava, R. S. and Srivastava, S. P. and Khare, B. B. Chain ratio type estimator for ratio of two population m3ans using auxiliary characters, Communications in Statistics-Theory and Methods, 18(10), 3917-3926, 1989.
• Srivastava, S. K. A generalized estimator for the mean of a finite population using multi- auxiliary information, Journal of the American Statistical Association, 66(334), 404-407, 1971.
• Srivenkataramana, T. A dual to ratio estimator in sample surveys, Biometrika, 67(1), 199- 204, 1980.
• Subramani, J. A new modified ratio estimator for estimation of population mean when median of the auxiliary variable is known, Pakistan Journal of Statistics and Operation Research, 9(2), 137-145, 2013.
• Subramani, J. and Kumarapandiyan, G. 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, 2012.
• Subramani, J. and Kumarapandiyan, G. Modified Ratio Estimators Using Known Median and co-efficient of Kurtosis, American Journal of Mathematics and Statistics, 2(4), 95-100, 2012.
• Subramani, J. and Kumarapandiyan, G. Estimation of Population Mean Using Known Median and Co-Efficent of Skewness, American Journal of Mathematics and Statistics, 2(5), 101-107, 2012.
• Subramani, J. and Kumarapandiyan, G. A class of modified ratio estimators using deciles of an auxiliary variable, International Journal of Statistics and Applications, 2(6), 101-107, 2012.
• Subramani, J. and Kumarapandiyan, G. Variance estimation using median of the auxiliary variable, International Journal of Probability and Statistics, 1(3), 36-40, 2012.
• Subramani, J. and Kumarapandiyan, G. Variance estimation using quartiles and their func- tions of an auxiliary variable, International Journal of Statistics and Applications, 2(5), 67-72, 2012.
• Tailor, R. and Sharma, B. K. A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis, Stat. Transition-new Ser, 10(1), 15-24, 2009.
• Upadhyaya, L. N. and Singh, H. P. Use of transformed auxiliary variable in estimating the finite population mean, Biometrical Journal, 41(5), 627-636, 1999.
• Yadav, S. K. and Kadilar, C. Efficient Family of Exponential Estimators for the Population Mean, Hacettepe journal of Mathematics and Statistics, 42(6), 671-677, 2013.
• Yan, Z. and Tian, B. Ratio method to the mean estimation using coefficient of skewness of auxiliary variable, Information Computing and Applications, Part II, CCIS 106, 103-110, 2010.
• Yasmeen, U. and Noor-ul-Amin, M. and Hanif, M. Generalized exponential estimators of - finite population mean using transformed auxiliary variables, International Journal of Applied and Computational Mathematics, 1(4), 589-598, 2015.