A Generalized Class of Estimators for Finite Population Mean Using Two Auxiliary Variables in Sample Surveys

  • Housila Prasad Singh School of Studies in Statistics, Vikram University, Ujjain-456010, M.P., India
  • Pragati Nigam Faculty of Agricultural Sciences, Mandsaur University, Mandsaur, M.P., India
Keywords: Auxiliary variable, study variable, bias, mean squared error, simple random sampling, stratified random sampling

Abstract

In this paper we have suggested a generalized class of estimators for estimating the finite population mean Y¯Y¯ of the study variable y using information on two auxiliary variables x and z. We have studied the properties of the proposed generalized class of estimators in simple random sampling without replacement scheme and in stratified random sampling up to the first order of approximation. It is shown that the suggested class of estimators is more efficient than the conventional unbiased estimator, ratio estimator, product estimator, traditional difference estimator, Srivastava (1967) estimator, Ray et al. (1979) estimator, Vos (1980) estimator, Upadhyaya et al. (1985) estimator, Rao (1991) estimator and Gupta and Shabbir (2008) estimator. Theoretical results are well supported through an empirical study.

Downloads

Download data is not yet available.

Author Biographies

Housila Prasad Singh, School of Studies in Statistics, Vikram University, Ujjain-456010, M.P., India

Housila Prasad Singh, born on 08/09/1957 in a village of Varanasi district of Uttar Pradesh. He did his M.Sc. (Statistics) in 1979 from Banaras Hindu University, Varanasi, U.P.. He obtained his M.Phil. (Applied Mathematics) in 1981 and Ph.D. (Applied Statistics) in 1985 from Indian School of Mines, Dhanbad, Bihar (Now Indian Institute of Technology, Dhanbad, Jharkhand). Currently he is a professor of Statistics, Vikram University, Ujjain, M.P.. He has 37 years of teaching experience and 41 years of research experience. He has been Head, School of Studies in Statistics, Dean, Faculty of Science and Executive Council Member of Vikram University, Ujjain, M.P. He has guided many students for their M.Sc. (02), M.Phil (18) and Ph.D. (23) degrees. He has been visiting scientist at University of Windsor, Windsor, Canada. He has published more than 510 research papers in journals of national and international repute. One of his research papers submitted for the award of “Dr. Radha Krishnan Samman 1992” has been appreciated by valuers. He has been awarded ‘Best Scientist Research Publication’ award (2009–10) and Out Standing Research Faculty by research faculty awards by Careers 360 as “One of the 10 Knowledge Producers in India” for academic year 2017–18. He has written two book reviews out of them one is published in Computational Statistics and Data Analysis (2000) and the other one in the Journal of Royal Statistical Society, Sr. A (2006). He is also the author of the Book “Randomness and Optimal Estimation in Data Sampling”, American Research Press, Rehoboth, USA. His area of research interest is Sampling Theory and Statistical Inference. Google Scholar (Citations by this date) is Citations-5653, h-index-35 and i10-index-134.

Pragati Nigam, Faculty of Agricultural Sciences, Mandsaur University, Mandsaur, M.P., India

Pragati Nigam, born on 27/11/1992 in Ujjain, M.P. She did her M.Sc. (Statistics) in 2015 (achieved II rank in the University) and Ph.D. (Statistics) in 2021 under the guidance of Prof. H. P. Singh, from School of Studies in Statistics, Vikram University, Ujjain. Presently she is working as Assistant Professor of Statistics at Faculty of Agricultural Sciences, Mandsaur University, Mandsaur. Dr. Pragati published 5 research papers and 1 book chapter (MKSES Publications) in national and international journals of repute.

References

Abu-Dayyeh, W. A., Ahmed, M. S., Ahmed, R. A. and Mutlak, H. A. (2003). Some estimators of a finite population mean using auxiliary information, Applied Mathematics and Computation, 139, 287–298.

Ahmed, M. S. (1997). The general class of chain estimators for ratio of two means using double sampling, Communications in Statistics-Theory and Methods, 26(9), 2249–2254.

Cochran, W. G. (1977). Sampling Techniques, Jhon Wiley and Sons, New York.

Das, A.K. and Tripathi, T. P. (1978). Use of auxiliary information in estimating the finite population variance, Sankhya, C, 40, 139–148.

Diana, G. (1993). A class of estimators of the population mean in stratified random sampling, Statistica, 53(1), 59–66.

Gleser, L. J. and Healy, J. D. (1976). Estimating the mean of a normal distribution with known coefficient of variation, Journal of American Statistical Association, 71, 977–981.

Gupta, S. and Shabbir, J. (2008). On estimating in estimating the population mean in simple random sampling, Journal of Applied Statistics, 35(5), 559–566.

Kadilar, C. and Cingi, H. (2003). Ratio estimator in stratified sampling, Biometrical Journal, 45, 218–225.

Koyuncu, N. (2013). Families of estimators for population mean using information on auxiliary attribute in stratified random sampling, Gazi University Journal of Sciences, 26(2), 181–193.

Koyuncu, N. (2016). Improved exponential type estimators for finite population mean in stratified random sampling, Pakistan Journal of Statistics and Operation Research, 12(3), 429–441.

Koyuncu, N. and Kadilar C. (2009). Family of estimators of population mean using two auxiliary variables in stratified sampling, Communications in Statistics-Theory and Methods, 38, 2398–2417.

Koyuncu, N. and Kadilar, C. (2010). On the family of estimators of population mean in stratified random sampling, Communications in Statistics-Theory and Methods, 26(2), 427–443.

Malik, S. and Singh, R. (2017). A new estimator for population mean using two auxiliary variables in stratified random sampling, Journal of Information and Optimization Sciences, 38(8), 1243–1252.

Mishra, M., Singh, B. P. and Singh, R. (2017). Estimation of population mean using two auxiliary variables in the stratified random sampling, Journal of Reliability and Statistical Studies, 10(1), 59–68.

Munner, S., Shabbir, J. and Khalil, A. (2016). Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables, Communications in Statistics-Theory and Methods, DOI:10.1080/03610926.2015.1035394.

Murthy, M. N. (1967). Sampling Theory and Methods, Statistical Publishing Society, India.

Olkin, I. (1958). Multivariate Ratio Estimation for Finite Population Biometrika, 45, 154–165.

Olufadi, Y. (2013). Dual to ratio-cum-product estimator in simple and stratified random sampling, Pakistan Journal of Statistics and Operation Research, 9(3), 305–319.

PCR (1998). Population Census Report of Multan District, Punjab Bureau of Statistics, Lahore, Pakistan.

Raj, D. (1965). On a method of using multiauxiliary information sample surveys, Journal of American Statistical Association, 60, 270–277.

Rao, P. S. R. S. and Mudholkar, G. D. (1967). Generalized multivariate estimator for the mean of finite populations, Journal of American Statistical Association, 62, 1009–1012.

Rao, T. J. (1991). On certain method of improving rations and regression estimators, Communications in Statistics, Theory and Methods, 20(10), 3325–3340.

Ray, S. K., Sahai, A. and Sahai, A. (1979). A note on ratio and product-type estimators, Annals of the Institute of Statistical Mathematics, 31, 141–144.

Reddy, V. N. (1978). A study on the use of prior knowledge on certain population parameters in estimation, Sankhya, C, 40, 29–34.

Searls, D. T. (1964). The utilization of a known coefficient of variation in the estimation procedure, Journal of American Statistical Association, 59, 1225–226.

Shabbir, J. (2018). Efficient utilisation of two auxiliary variables in stratified double sampling, Communications in Statistics-Theory and Methods, 47(1), 92–101.

Shabbir, J. and Gupta, S. (2005). Improved ratio estimators in stratified sampling, American Journal of Mathematics and Management Sciences, 25(3–4), 293–311.

Shabbir, J. and Gupta, S. (2015). Estimation of finite population mean using two auxiliary variables in stratified two-phase sampling, Communications in Statistics-Simulation and Computation, DOI:10.1080/03610918.2014.995817.

Shabbir, J. and Gupta, S. (2016). Estimation of population coefficient of variation in simple and stratified random sampling under two-phase sampling scheme when using two auxiliary variables, Communications in Statistics-Theory and Methods, DOI:10.1080/03610926.2016.1175627.

Sharma, P. and Singh, R. (2014). Improved ratio-type estimators using two auxiliary variables under second order approximation, Mathematical Journal of Interdisciplinary Sciences, 2(2), 193–204.

Sharma, P. and Singh, R. (2015). A class of exponential ratio estimators of finite population mean using two auxiliary variables, Pakistan Journal of Statistics and Operation Research, 11(2), 221–229.

Shukla, G. K. (1966). An alternative multivariate ratio estimator for finite population, Calcutta Statistical Association Bulletin, 15, 127–134.

Singh, D. and Chaudhary, F. S. (1986). Theory and Analysis of Sample Survey Designs, Jhon Wiley and Sons, New York.

Singh, H. P. (1986). A Generalized class of estimators of ratio, product and mean using supplementary information on an auxiliary character in PPSWR sampling scheme, Gujarat Statistical Review, 13(2), 1–30.

Singh, H. P. and Tailor, R. (2005). Estimation of finite population mean using known correlation coefficient between auxiliary characters, Statistica, anno LXV, 4, 407–418.

Singh, H. P. and Vishwakarma, G. K. (2008). A family of estimators of population mean using auxiliary formation in stratified sampling, Communications in Statistics-Theory and Methods, 37(7), 1038–1050.

Singh, H. P., Upadhyaya, L. N. and Tailor, R. (2009). Ratio-cum-product type exponential estimator, Statistica, anno LXIX, 4, 300–310.

Singh, M. P. (1967). Ratio-cum-product method of estimation, Metrika, 12(1), 34–62.

Singh, M. P. (1969). Comparison of some ratio-cum-product estimators, Sankhya, series B, 31, 375–378.

Singh, R. and Kumar, M. (2012). Improved estimators of population mean using two auxiliary variables in stratified random sampling, Pakistan Journal of Statistics and Operation Research, 8, 65–72.

Singh, R., Chouhan, P. and Sawan, N. (2008). On linear combination of ratio-product-type exponential estimator for estimating finite population mean, Statistics in Transition, 9(1), 105–115.

Singh, S. (2003). Advanced sampling theory with applications- How michel “selected” Amy, Kluwer Academic Publishers, I edition volume I and II.

Srivastava, S. K. (1965). An estimation of the mean of a finite population using several auxiliary variables, Journal of the Indian Statistical Association 3, 189–194.

Srivastava, S. K. (1966). A note on Olkin’s multivariate ratio estimator, Journal of Indian Statistical Association, 4, 202–208.

Srivastava, S. K. (1967). An estimator using auxiliary information in sample surveys, Culcutta Statistical Association, 16, 121–132.

Srivastava, S. K. (1971). A generalized estimator for the mean of a finite population using multiauxiliary information, Journal of American Statistical Association, 66, 404–407.

Srivenkataramana, T. and Tracy, D. S. (1984). Positive and negative valued auxiliary variates in surveys, Metron, XLII, (3–4), 3–14.

Steel, R. G. D. and Torrie, J, H. (1960). Principles and Procedures of Statistics, McGraw Hill Book Co.

Swain, A. K. P. C. (2013). On some modified ratio and product-type estimators. Revisited, Investigacion operational, 34(1), 35–57.

Tailor, R. and Chouhan, S. (2014). Ratio-cum-product-type exponential estimator of finite population mean in stratified random sampling, Communications in Statistics-Theory and Methods, 43(2), 343–354.

Tailor, R., Chouhan, S., Tailor, R. and Garg, N. (2012). A ratio-cum-product estimator of population mean in stratified random sampling using two auxiliary variables, Statistica, anno LXXII, n.3, 287–297.

Tripathi, T. P., Maiti, P. and Sharma, S. D. (1983). Use of prior information on some parameter in estimating population mean, Sankhaya, A, 45(3), 372–376.

Upadhyaya, L. N., Singh, H. P., and Vos, J. W. E. (1985). On the estimation of population means and ratios using supplementary information, Statistica Neerlandica, 39, 309–318.

Verma, H. K., Sharma, P. and Singh, R. (2015). Some families of estimators using two auxiliary variables in a stratified random sampling, Revista Investigacion Operacional, 36(2), 140–150.

Vos, J. W. E. (1980). Mixing of direct, ratio and product method estimators, Statistica Neerlandica, 34, 209–218.

Yadav, S. K., Mishra, S., Kadilar, C. and Shukla, A. K. (2015a). Improved dual to ratio cum dual to product estimator in the stratified random sampling, American Journal of Operational Research, 5(3), 57–63.

Yadav, S. K., Mishra, S., Mishra, S. S. and Shukla, A. K. (2015b). Searching efficient estimator of population mean in stratified random sampling, American Journal of Operational Research, 5(4), 75–81.

Published
2022-02-22
Section
Articles