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Classes of Population Mean Estimators using Transformed Variables in Double Sampling

Year 2023, , 1834 - 1852, 01.12.2023
https://doi.org/10.35378/gujs.1056453

Abstract

Transformation techniques have been used to increase the efficiency of estimators in sample surveys. In this paper, some classes of population mean estimators using transformation on an auxiliary variable and on both the auxiliary and study variables have been proposed under double sampling. The proposed estimators’ biases and mean square errors are approximated up to the first order. A simulation study and application to a rubber production dataset have been used to illustrate the proposed estimators’ performance. The results show that they perform much better than other existing estimators under given conditions.

Supporting Institution

National Science, Research and Innovation Fund (NSRF), and King Mongkut’s University of Technology North Bangkok

Project Number

KMUTNB-FF-65-28

References

  • [1] Cochran, W. G., “Sampling Techniques”, 3rd edition, India: Wiley Eastern Limited, (1940).
  • [2] Murthy, M. N., “Sampling Theory and Methods”, India: Statistical Publishing Society, (1967).
  • [3] Sisodia, B. V., Dwivedi, V. K., “A modified ratio estimator using coefficient of variation of auxiliary variable”, Journal Indian Society of Agricultural Statistics, 8(1): 20-25, (1981).
  • [4] Upadhyaya, L. N., Singh, H. P., “Use of transformed auxiliary variable in estimating the finite population mean”, Biometrical Journal, 41(5): 627-636, (1999).
  • [5] Singh, G. N., “On the improvement of product method of estimation in sample surveys”, Journal of the Indian Society of Agricultural Statistics, 56(3): 267-275, (2003).
  • [6] Singh, H. P., Tailor, R., “Use of known correlation co-efficient in estimating the finite population means”, Statistics in Transition, 6(4): 555-560, (2003).
  • [7] Singh, H. P., Tailor, R., Tailor, R., and Kakran, M. S., “An improved estimator of population mean using power transformation”, Journal of the Indian Society of Agricultural Statistics, 58(2): 223-230, (2004).
  • [8] Kadilar, C., Cingi, H., “Ratio estimators in simple random sampling”, Applied Mathematics and Computation, 151(3): 893-902, (2004).
  • [9] Kadilar, C., Cingi, H., “New ratio estimators using correlation coefficient”, Interstat, 4: 1-11, (2006).
  • [10] Kadilar, C., 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).
  • [11] Yan, Z., Tian, B., “Ratio method to the mean estimation using coefficient of skewness of auxiliary variable”, Proceeding of the ICICA 2010, Part II, CCIS 106: 103-111, (2010).
  • [12] Subramani, J., Kumarapandiyan, G., “A class of almost unbiased modified ratio estimators for population mean with known population parameters”, Elixir Statistics, 44: 7411-7415, (2012).
  • [13] Subramani, J., Kumarapandiyan, G., “Estimation of population mean using coefficient of variation and median of an auxiliary variable”, International Journal of Probability and Statistics, 1: 111-118, (2012).
  • [14] Subramani, J., Kumarapandiyan, G., “Estimation of population mean using known median and coefficient of skewness”, American Journal of Mathematics and Statistics, 2: 101-107, (2012).
  • [15] Subramani, J., Kumarapandiyan, G., “Modified ratio estimators using known median and co-efficient of kurtosis”, American Journal of Mathematics and Statistics, 2: 95-100, (2012).
  • [16] Raja, T. A., Subair, M., Maqbool, S., and Hakak, A., “Enhancing the mean ratio estimator for estimating population mean using conventional parameters”, International Journal of Mathematics and Statistics Invention, 5(1): 58-61, (2017).
  • [17] Neyman, J., “Contribution to the theory of sampling human populations”, Journal of the American Statistical Association, 33: 101-116, (1938).
  • [18] Malik, K. A., Tailor, R., “Ratio type estimator of population mean in double sampling”, International Journal of Advanced Mathematics and Statistics, 1(1): 34-39, (2013).
  • [19] Amin, M. N. U., Shahbaz, M. Q., and Kadilar, C., “Ratio estimators for population mean using robust regression in double sampling”, Gazi University Journal of Science, 29(4): 793-798, (2016).
  • [20] Akingbade, T. J., Okafor, F. C., “A class of ratio type estimators in double sampling using an auxiliary variable with some known population parameters”, Journal of the Nigerian Statistical Association, 30: 14-29, (2018).
  • [21] Mohanty, S., “Combination of regression and ratio estimate”, Journal of the Indian Statistical Association, 5: 16-19, (1967).
  • [22] Chand, L., “Some Ratio-type Estimators based on two or more Auxiliary Variables”, Phd.Thesis, Iowa State University, Iowa, (1975).
  • [23] Kiregyera, B., “A chain ratio-type estimator in finite population double sampling using two auxiliary variables”, Metrika, 27: 217-223, (1980).
  • [24] Kiregyera, B., “Regression-type estimator using two auxiliary variables and model of double sampling from finite populations”, Metrika, 31: 215-226, (1984).
  • [25] Bedi, P. K., “On two-phase multivariate sampling estimator”, Journal of the Indian Society of Agricultural Statistics, 37(2): 158-162, (1985).
  • [26] Srivastava, S. Rani, Khare, B. B., and Srivastava, S. R., “A generalized chain ratio estimator for mean of finite population”, Journal of the Indian Society of Agricultural Statistics, 42(1): 108-117, (1990).
  • [27] Singh, G. N., “On the use of transformed auxiliary variable in the estimation of population mean in two phase sampling”, Statistics in Transition, 5(3): 405-416, (2001).
  • [28] Singh, H. P., Upadhyaya, L. N., and Chandra, P., “A general family of estimators for estimating population mean using two auxiliary variables in two-phase sampling”, Statistics in Transition, 6(7): 1055-1077, (2004).
  • [29] Samiuddin, M., Hanif, M., “Estimation of population mean in single and two phase sampling with or without additional information”, Pakistan Journal of Statistics, 23(2): 99-118, (2007).
  • [30] Singh, R., Chuhan, P., and Sawan, N., “A family of estimators for estimating population mean using known correlation coefficient in two phase sampling”, Statistics in Transition, 8(1): 89-96, (2007).
  • [31] Singh, H. P., Agnihotri, N., “A general procedure of estimating population mean using auxiliary information in sample survey”, Statistics in Transition, 9(1): 71-87, (2008).
  • [32] Zaman, T., Kadilar, C., “New class of exponential estimators for finite population mean in two-phase sampling”, Communications in Statistics-Theory and Methods, 50(4): 874-889, (2021).
  • [33] Zaman, T., Kadilar, C., “Exponential ratio and product type estimators of the mean in stratified two-phase sampling”, AIMS Mathematics, 6(5): 4265-4279, (2021).
  • [34] Srivenkataramana, T., “A dual to ratio estimator in sample surveys”, Biometrika, 67: 199-204, (1980).
  • [35] Bandyopadhyaya, S., “Improved ratio and product estimators”, Sankhya, Series C, 42: 45-49, (1980).
  • [36] Singh, H. P., Upadhyaya, L. N., “A dual to modified ratio estimator using coefficient of variation of auxiliary variable”, Proceedings of the National Academy of Sciences, India-Section A, 56(A): 336-340, (1986).
  • [37] Onyeka, A. C., Nlebedim, V. U., and Izunobi, C. H., “Estimation of population ratio in simple random sampling using variable transformation”, Global Journal of Science Frontier Research Mathematics and Decision Sciences, 13(4): 57-65, (2013).
  • [38] Adewara, A. A., “Effect of improving both the auxiliary and variable of interest in ratio and product estimators”, Proceedings of the Pakistan Academy of Sciences, 43(4): 275-278, (2006).
  • [39] Adewara, A. A., Singh, R., and Kumar, M., “Efficiency of some modified ratio and product estimators using known value of some population parameters”, International Journal of Applied Science and Technology, 2(2): 76-79, (2012).
  • [40] Singh, R., Malik, S., and Smarandache, F., Uses of Sampling Techniques & Inventory Control with Capacity Constraints, Malik, S., Kumar, N., and Smarandache, F. editors, Pons Editions, Belgium, 19-29, (2016).
  • [41] Thongsak, N., Lawson, N., “Classes of dual to modified ratio estimators for estimating population mean in simple random sampling”, Proceeding of the 2021 Research, Invention and Innovation Congress, 211-215, (2021).
  • [42] Kumar, M., Bahl, S., “Class of dual to ratio estimators for double sampling”, Statistical Papers, 47: 319-326, (2006).
  • [43] Singh, B. K., Choudhury, S., “Dual to product estimator for estimating population mean in double sampling”, International Journal of Statistics and Systems, 7: 31-39, (2012).
  • [44] Choudhury, S., Singh, B. K., “Study of dual to ratio-cum-product estimator of finite population mean under double sampling in sample surveys”, Journal of Statistical Theory and Applications, 14(2): 214-221, (2015).
  • [45] Boonrodrak, N., “Ratio estimators of population mean using transformed auxiliary variable under two-phase sampling”, MSc.Thesis, King Mongkut’s University of Technology North Bangkok, Bangkok, (2015).
  • [45] Jaroengeratikun, U., Lawson, N., “Improved ratio estimators of population mean using transformed variable in double sampling”, The Journal of Applied Science, 17(2): 9-18, (2018).
  • [47] Kamba, A. I., Adewara, A. A., and Ahmed, A., “Modification of ratio estimator under two phase sampling”, FUW Trends in Science & Technology Journal, 4: 495-500, (2019).
  • [48] Cochran, W. G., “Sampling Techniques”, New York: John Wiley and Sons, (1977).
  • [49] http://www.oae.go.th/assets/portals/1/fileups/prcaidata/files/1_rubber_dit%2060.pdf. Access date: 16.09.2020.
Year 2023, , 1834 - 1852, 01.12.2023
https://doi.org/10.35378/gujs.1056453

Abstract

Project Number

KMUTNB-FF-65-28

References

  • [1] Cochran, W. G., “Sampling Techniques”, 3rd edition, India: Wiley Eastern Limited, (1940).
  • [2] Murthy, M. N., “Sampling Theory and Methods”, India: Statistical Publishing Society, (1967).
  • [3] Sisodia, B. V., Dwivedi, V. K., “A modified ratio estimator using coefficient of variation of auxiliary variable”, Journal Indian Society of Agricultural Statistics, 8(1): 20-25, (1981).
  • [4] Upadhyaya, L. N., Singh, H. P., “Use of transformed auxiliary variable in estimating the finite population mean”, Biometrical Journal, 41(5): 627-636, (1999).
  • [5] Singh, G. N., “On the improvement of product method of estimation in sample surveys”, Journal of the Indian Society of Agricultural Statistics, 56(3): 267-275, (2003).
  • [6] Singh, H. P., Tailor, R., “Use of known correlation co-efficient in estimating the finite population means”, Statistics in Transition, 6(4): 555-560, (2003).
  • [7] Singh, H. P., Tailor, R., Tailor, R., and Kakran, M. S., “An improved estimator of population mean using power transformation”, Journal of the Indian Society of Agricultural Statistics, 58(2): 223-230, (2004).
  • [8] Kadilar, C., Cingi, H., “Ratio estimators in simple random sampling”, Applied Mathematics and Computation, 151(3): 893-902, (2004).
  • [9] Kadilar, C., Cingi, H., “New ratio estimators using correlation coefficient”, Interstat, 4: 1-11, (2006).
  • [10] Kadilar, C., 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).
  • [11] Yan, Z., Tian, B., “Ratio method to the mean estimation using coefficient of skewness of auxiliary variable”, Proceeding of the ICICA 2010, Part II, CCIS 106: 103-111, (2010).
  • [12] Subramani, J., Kumarapandiyan, G., “A class of almost unbiased modified ratio estimators for population mean with known population parameters”, Elixir Statistics, 44: 7411-7415, (2012).
  • [13] Subramani, J., Kumarapandiyan, G., “Estimation of population mean using coefficient of variation and median of an auxiliary variable”, International Journal of Probability and Statistics, 1: 111-118, (2012).
  • [14] Subramani, J., Kumarapandiyan, G., “Estimation of population mean using known median and coefficient of skewness”, American Journal of Mathematics and Statistics, 2: 101-107, (2012).
  • [15] Subramani, J., Kumarapandiyan, G., “Modified ratio estimators using known median and co-efficient of kurtosis”, American Journal of Mathematics and Statistics, 2: 95-100, (2012).
  • [16] Raja, T. A., Subair, M., Maqbool, S., and Hakak, A., “Enhancing the mean ratio estimator for estimating population mean using conventional parameters”, International Journal of Mathematics and Statistics Invention, 5(1): 58-61, (2017).
  • [17] Neyman, J., “Contribution to the theory of sampling human populations”, Journal of the American Statistical Association, 33: 101-116, (1938).
  • [18] Malik, K. A., Tailor, R., “Ratio type estimator of population mean in double sampling”, International Journal of Advanced Mathematics and Statistics, 1(1): 34-39, (2013).
  • [19] Amin, M. N. U., Shahbaz, M. Q., and Kadilar, C., “Ratio estimators for population mean using robust regression in double sampling”, Gazi University Journal of Science, 29(4): 793-798, (2016).
  • [20] Akingbade, T. J., Okafor, F. C., “A class of ratio type estimators in double sampling using an auxiliary variable with some known population parameters”, Journal of the Nigerian Statistical Association, 30: 14-29, (2018).
  • [21] Mohanty, S., “Combination of regression and ratio estimate”, Journal of the Indian Statistical Association, 5: 16-19, (1967).
  • [22] Chand, L., “Some Ratio-type Estimators based on two or more Auxiliary Variables”, Phd.Thesis, Iowa State University, Iowa, (1975).
  • [23] Kiregyera, B., “A chain ratio-type estimator in finite population double sampling using two auxiliary variables”, Metrika, 27: 217-223, (1980).
  • [24] Kiregyera, B., “Regression-type estimator using two auxiliary variables and model of double sampling from finite populations”, Metrika, 31: 215-226, (1984).
  • [25] Bedi, P. K., “On two-phase multivariate sampling estimator”, Journal of the Indian Society of Agricultural Statistics, 37(2): 158-162, (1985).
  • [26] Srivastava, S. Rani, Khare, B. B., and Srivastava, S. R., “A generalized chain ratio estimator for mean of finite population”, Journal of the Indian Society of Agricultural Statistics, 42(1): 108-117, (1990).
  • [27] Singh, G. N., “On the use of transformed auxiliary variable in the estimation of population mean in two phase sampling”, Statistics in Transition, 5(3): 405-416, (2001).
  • [28] Singh, H. P., Upadhyaya, L. N., and Chandra, P., “A general family of estimators for estimating population mean using two auxiliary variables in two-phase sampling”, Statistics in Transition, 6(7): 1055-1077, (2004).
  • [29] Samiuddin, M., Hanif, M., “Estimation of population mean in single and two phase sampling with or without additional information”, Pakistan Journal of Statistics, 23(2): 99-118, (2007).
  • [30] Singh, R., Chuhan, P., and Sawan, N., “A family of estimators for estimating population mean using known correlation coefficient in two phase sampling”, Statistics in Transition, 8(1): 89-96, (2007).
  • [31] Singh, H. P., Agnihotri, N., “A general procedure of estimating population mean using auxiliary information in sample survey”, Statistics in Transition, 9(1): 71-87, (2008).
  • [32] Zaman, T., Kadilar, C., “New class of exponential estimators for finite population mean in two-phase sampling”, Communications in Statistics-Theory and Methods, 50(4): 874-889, (2021).
  • [33] Zaman, T., Kadilar, C., “Exponential ratio and product type estimators of the mean in stratified two-phase sampling”, AIMS Mathematics, 6(5): 4265-4279, (2021).
  • [34] Srivenkataramana, T., “A dual to ratio estimator in sample surveys”, Biometrika, 67: 199-204, (1980).
  • [35] Bandyopadhyaya, S., “Improved ratio and product estimators”, Sankhya, Series C, 42: 45-49, (1980).
  • [36] Singh, H. P., Upadhyaya, L. N., “A dual to modified ratio estimator using coefficient of variation of auxiliary variable”, Proceedings of the National Academy of Sciences, India-Section A, 56(A): 336-340, (1986).
  • [37] Onyeka, A. C., Nlebedim, V. U., and Izunobi, C. H., “Estimation of population ratio in simple random sampling using variable transformation”, Global Journal of Science Frontier Research Mathematics and Decision Sciences, 13(4): 57-65, (2013).
  • [38] Adewara, A. A., “Effect of improving both the auxiliary and variable of interest in ratio and product estimators”, Proceedings of the Pakistan Academy of Sciences, 43(4): 275-278, (2006).
  • [39] Adewara, A. A., Singh, R., and Kumar, M., “Efficiency of some modified ratio and product estimators using known value of some population parameters”, International Journal of Applied Science and Technology, 2(2): 76-79, (2012).
  • [40] Singh, R., Malik, S., and Smarandache, F., Uses of Sampling Techniques & Inventory Control with Capacity Constraints, Malik, S., Kumar, N., and Smarandache, F. editors, Pons Editions, Belgium, 19-29, (2016).
  • [41] Thongsak, N., Lawson, N., “Classes of dual to modified ratio estimators for estimating population mean in simple random sampling”, Proceeding of the 2021 Research, Invention and Innovation Congress, 211-215, (2021).
  • [42] Kumar, M., Bahl, S., “Class of dual to ratio estimators for double sampling”, Statistical Papers, 47: 319-326, (2006).
  • [43] Singh, B. K., Choudhury, S., “Dual to product estimator for estimating population mean in double sampling”, International Journal of Statistics and Systems, 7: 31-39, (2012).
  • [44] Choudhury, S., Singh, B. K., “Study of dual to ratio-cum-product estimator of finite population mean under double sampling in sample surveys”, Journal of Statistical Theory and Applications, 14(2): 214-221, (2015).
  • [45] Boonrodrak, N., “Ratio estimators of population mean using transformed auxiliary variable under two-phase sampling”, MSc.Thesis, King Mongkut’s University of Technology North Bangkok, Bangkok, (2015).
  • [45] Jaroengeratikun, U., Lawson, N., “Improved ratio estimators of population mean using transformed variable in double sampling”, The Journal of Applied Science, 17(2): 9-18, (2018).
  • [47] Kamba, A. I., Adewara, A. A., and Ahmed, A., “Modification of ratio estimator under two phase sampling”, FUW Trends in Science & Technology Journal, 4: 495-500, (2019).
  • [48] Cochran, W. G., “Sampling Techniques”, New York: John Wiley and Sons, (1977).
  • [49] http://www.oae.go.th/assets/portals/1/fileups/prcaidata/files/1_rubber_dit%2060.pdf. Access date: 16.09.2020.
There are 49 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Statistics
Authors

Natthapat Thongsak This is me 0000-0002-8815-5191

Nuanpan Lawson 0000-0001-8318-5474

Project Number KMUTNB-FF-65-28
Publication Date December 1, 2023
Published in Issue Year 2023

Cite

APA Thongsak, N., & Lawson, N. (2023). Classes of Population Mean Estimators using Transformed Variables in Double Sampling. Gazi University Journal of Science, 36(4), 1834-1852. https://doi.org/10.35378/gujs.1056453
AMA Thongsak N, Lawson N. Classes of Population Mean Estimators using Transformed Variables in Double Sampling. Gazi University Journal of Science. December 2023;36(4):1834-1852. doi:10.35378/gujs.1056453
Chicago Thongsak, Natthapat, and Nuanpan Lawson. “Classes of Population Mean Estimators Using Transformed Variables in Double Sampling”. Gazi University Journal of Science 36, no. 4 (December 2023): 1834-52. https://doi.org/10.35378/gujs.1056453.
EndNote Thongsak N, Lawson N (December 1, 2023) Classes of Population Mean Estimators using Transformed Variables in Double Sampling. Gazi University Journal of Science 36 4 1834–1852.
IEEE N. Thongsak and N. Lawson, “Classes of Population Mean Estimators using Transformed Variables in Double Sampling”, Gazi University Journal of Science, vol. 36, no. 4, pp. 1834–1852, 2023, doi: 10.35378/gujs.1056453.
ISNAD Thongsak, Natthapat - Lawson, Nuanpan. “Classes of Population Mean Estimators Using Transformed Variables in Double Sampling”. Gazi University Journal of Science 36/4 (December 2023), 1834-1852. https://doi.org/10.35378/gujs.1056453.
JAMA Thongsak N, Lawson N. Classes of Population Mean Estimators using Transformed Variables in Double Sampling. Gazi University Journal of Science. 2023;36:1834–1852.
MLA Thongsak, Natthapat and Nuanpan Lawson. “Classes of Population Mean Estimators Using Transformed Variables in Double Sampling”. Gazi University Journal of Science, vol. 36, no. 4, 2023, pp. 1834-52, doi:10.35378/gujs.1056453.
Vancouver Thongsak N, Lawson N. Classes of Population Mean Estimators using Transformed Variables in Double Sampling. Gazi University Journal of Science. 2023;36(4):1834-52.