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Variance estimation using Bernoulli auxiliary variable for time-scaled survey

Year 2025, Volume: 54 Issue: 2, 779 - 796, 28.04.2025

Prayas Sharma , Mamta Kumari

https://doi.org/10.15672/hujms.1580875

Abstract

The diversity in the qualities under investigation is necessary to comprehend any phenomenon, whether in a real-world or practical setting. It is crucial to know the differences between current and previous circumstances. Therefore, to estimate the population variance with dichotomous auxiliary information, the exponentially weighted moving average statistic is used. This manuscript suggests a generalized class of memory-type estimators for the estimation of population variance using the Bernoulli auxiliary variable under time-scaled survey. The properties of the suggested class of memory type estimator and exponentially weighted moving average version of the usual ratio, regression, and exponential estimators are derived up to the first order of approximation. It has been shown through empirical and simulation study that the suggested estimator is more efficient than the usual estimators and the exponentially weighted moving average version of the estimators in the literature.

Keywords

Auxiliary attribute exponentially weighted moving average statistic mean squared error memory type estimator variance estimation.

References

  • [1] N.K. Adichwal, P. Sharma, and R. Singh, Generalized class of estimators for population variance using information on two auxiliary variables, Int. Jour. of Appl. and Comp.Math. 3, 651661, 2017.
  • [2] N.K. Adichwal, P. Sharma, H.K. Verma, and R. Singh, Generalized class of estimators for population variance using auxiliary attribute, Int. Jour. of Appl. and Comp.Math. 2, 499508, 2016.
  • [3] I. Aslam, M.N. Amin, A. Mahmood, and P. Sharma, New memory-based ratio estimator in survey sampling, Natu.and Appl.Sci.Int. Jour. (NASIJ) 5 (1), 168181, 2024.
  • [4] I. Aslam, M. Noor-ul Amin, M. Hanif, and P. Sharma, Memory type ratio and product estimators under ranked-based sampling schemes, Comm.in Stat.-Theo.and Meth. 52 (4), 11551177, 2023.
  • [5] M.A. Bhat, S. Maqbool, and M. Subzar, An improvement in variance estimator for the estimation of population variance, using known values of auxiliary information, Int. Jour.of Pure & App. Biosci.6 (5), 135138, 2018.
  • [6] S. Bhushan, A. Kumar, A. Alrumayh, H.A. Khogeer, and R. Onyango, Evaluating the performance of memory type logarithmic estimators using simple random sampling, Plos One 17 (12), e0278264, 2022.
  • [7] A.K. Das, Use of auxiliary information in estimating the finite population variance, Sankhya, C 40, 139148, 1978.
  • [8] C.T. Isaki, Variance estimation using auxiliary information, JASA 78 (381), 117123, 1983.
  • [9] N. Koyuncu, Efficient estimators of population mean using auxiliary attributes, App. Math. and Comp. 218 (22), 1090010905, 2012.
  • [10] S. Malik and R. Singh, An improved estimator using two auxiliary attributes, App.Math.and Comp.219 (23), 1098310986, 2013.
  • [11] P. Mukhopadhyay, Theory and methods of survey sampling, PHI Learning Pvt. Ltd., 2008.
  • [12] M. Noor-ul Amin, Memory type ratio and product estimators for population mean for time-based surveys, Jour. of Stat. Comp. and Simu.90 (17), 30803092, 2020.
  • [13] M. Noor-ul Amin, Memory type estimators of population mean using exponentially weighted moving averages for time scaled surveys, Comm.in Stat.-Theo.and Meth. 50 (12), 27472758, 2021.
  • [14] M. Noor-ul Amin, A. Safeer, and P. Sharma, Variable acceptance sampling plan based on hybrid exponentially weighted moving averages, Comm.in Stat.-Simu. and Comp. 51 (12), 75447553, 2022.
  • [15] M.N. Qureshi, M.U. Tariq, and M. Hanif, Memory-type ratio and product estimators for population variance using exponentially weighted moving averages for time-scaled surveys, Comm.in Stat.-Simu. and Comp. 53 (3), 14841493, 2024.
  • [16] P. Sharma and R. Singh, Efficient estimator of population mean in stratified random sampling using auxiliary attribute, Wor.App.Sci Jour. 27 (12), 17861791, 2013.
  • [17] P. Sharma and R. Singh, Improved estimators in simple random sampling when study variable is an attribute, Jour.of Stat. App. and Pro. Lett. 2 (1), 5158, 2015.
  • [18] P. Sharma, H.K. Verma, S. Singh, and C.N. Bouza, Estimators for population variance using auxiliary information on quartile, Inves.Oper.39 (4), 2018.
  • [19] R. Singh, M. Kumar, A.K. Singh, and F. Smarandache, A family of estimators of population variance using information on auxiliary attribute, IN SAM ME SER, 63, 2011.
  • [20] R. Singh and S. Malik, Improved estimation of population variance using information on auxiliary attribute in simple random sampling, Appl. Math. and Comp. 235, 4349, 2014.
  • [21] T. Zaman and H. Bulut, An efficient family of robust-type estimators for the population variance in simple and stratified random sampling, Comm.in Stat.-Theo.and Meth. 52 (8), 26102624, 2023.
  • [22] G. Özel, H. Çıngı, and M. Oguz, Separate ratio estimators for the population variance in stratified random sampling, Comm.in Stat.-Theo.and Meth. 43 (22), 47664779, 2014.
  • [23] G. Ö. Kadılar, A new exponential type estimator for the population mean in simple random sampling, JMASM 15, 207214, 2016.
  • [24] G. Özel and C. Kadılar, Modified Exponential Type Estimators for Population Mean in Stratified Random Sampling: An Application on the Geometric Distributed Aftershocks, Co-chair, 63.
  • [25] M. U. Tariq, M. N. Qureshi, O. A. Alamri, S. Iftikhar, B. S. Alsaedi, and M. Hanif, Variance estimation using memory type estimators based on EWMA statistic for time scaled surveys in stratified sampling, Sci.Rep. 14 (1), 26700, 2024.
  • [26] P. V. Sukhatme and B. V. Sukhatme, Sampling theory of surveys with applications, 1970.
  • [27] P. Mukhopadhyay, Theory and methods of survey sampling, PHI Learning Pvt. Ltd., 2008.

Year 2025, Volume: 54 Issue: 2, 779 - 796, 28.04.2025

Prayas Sharma , Mamta Kumari

https://doi.org/10.15672/hujms.1580875

Abstract

References

  • [1] N.K. Adichwal, P. Sharma, and R. Singh, Generalized class of estimators for population variance using information on two auxiliary variables, Int. Jour. of Appl. and Comp.Math. 3, 651661, 2017.
  • [2] N.K. Adichwal, P. Sharma, H.K. Verma, and R. Singh, Generalized class of estimators for population variance using auxiliary attribute, Int. Jour. of Appl. and Comp.Math. 2, 499508, 2016.
  • [3] I. Aslam, M.N. Amin, A. Mahmood, and P. Sharma, New memory-based ratio estimator in survey sampling, Natu.and Appl.Sci.Int. Jour. (NASIJ) 5 (1), 168181, 2024.
  • [4] I. Aslam, M. Noor-ul Amin, M. Hanif, and P. Sharma, Memory type ratio and product estimators under ranked-based sampling schemes, Comm.in Stat.-Theo.and Meth. 52 (4), 11551177, 2023.
  • [5] M.A. Bhat, S. Maqbool, and M. Subzar, An improvement in variance estimator for the estimation of population variance, using known values of auxiliary information, Int. Jour.of Pure & App. Biosci.6 (5), 135138, 2018.
  • [6] S. Bhushan, A. Kumar, A. Alrumayh, H.A. Khogeer, and R. Onyango, Evaluating the performance of memory type logarithmic estimators using simple random sampling, Plos One 17 (12), e0278264, 2022.
  • [7] A.K. Das, Use of auxiliary information in estimating the finite population variance, Sankhya, C 40, 139148, 1978.
  • [8] C.T. Isaki, Variance estimation using auxiliary information, JASA 78 (381), 117123, 1983.
  • [9] N. Koyuncu, Efficient estimators of population mean using auxiliary attributes, App. Math. and Comp. 218 (22), 1090010905, 2012.
  • [10] S. Malik and R. Singh, An improved estimator using two auxiliary attributes, App.Math.and Comp.219 (23), 1098310986, 2013.
  • [11] P. Mukhopadhyay, Theory and methods of survey sampling, PHI Learning Pvt. Ltd., 2008.
  • [12] M. Noor-ul Amin, Memory type ratio and product estimators for population mean for time-based surveys, Jour. of Stat. Comp. and Simu.90 (17), 30803092, 2020.
  • [13] M. Noor-ul Amin, Memory type estimators of population mean using exponentially weighted moving averages for time scaled surveys, Comm.in Stat.-Theo.and Meth. 50 (12), 27472758, 2021.
  • [14] M. Noor-ul Amin, A. Safeer, and P. Sharma, Variable acceptance sampling plan based on hybrid exponentially weighted moving averages, Comm.in Stat.-Simu. and Comp. 51 (12), 75447553, 2022.
  • [15] M.N. Qureshi, M.U. Tariq, and M. Hanif, Memory-type ratio and product estimators for population variance using exponentially weighted moving averages for time-scaled surveys, Comm.in Stat.-Simu. and Comp. 53 (3), 14841493, 2024.
  • [16] P. Sharma and R. Singh, Efficient estimator of population mean in stratified random sampling using auxiliary attribute, Wor.App.Sci Jour. 27 (12), 17861791, 2013.
  • [17] P. Sharma and R. Singh, Improved estimators in simple random sampling when study variable is an attribute, Jour.of Stat. App. and Pro. Lett. 2 (1), 5158, 2015.
  • [18] P. Sharma, H.K. Verma, S. Singh, and C.N. Bouza, Estimators for population variance using auxiliary information on quartile, Inves.Oper.39 (4), 2018.
  • [19] R. Singh, M. Kumar, A.K. Singh, and F. Smarandache, A family of estimators of population variance using information on auxiliary attribute, IN SAM ME SER, 63, 2011.
  • [20] R. Singh and S. Malik, Improved estimation of population variance using information on auxiliary attribute in simple random sampling, Appl. Math. and Comp. 235, 4349, 2014.
  • [21] T. Zaman and H. Bulut, An efficient family of robust-type estimators for the population variance in simple and stratified random sampling, Comm.in Stat.-Theo.and Meth. 52 (8), 26102624, 2023.
  • [22] G. Özel, H. Çıngı, and M. Oguz, Separate ratio estimators for the population variance in stratified random sampling, Comm.in Stat.-Theo.and Meth. 43 (22), 47664779, 2014.
  • [23] G. Ö. Kadılar, A new exponential type estimator for the population mean in simple random sampling, JMASM 15, 207214, 2016.
  • [24] G. Özel and C. Kadılar, Modified Exponential Type Estimators for Population Mean in Stratified Random Sampling: An Application on the Geometric Distributed Aftershocks, Co-chair, 63.
  • [25] M. U. Tariq, M. N. Qureshi, O. A. Alamri, S. Iftikhar, B. S. Alsaedi, and M. Hanif, Variance estimation using memory type estimators based on EWMA statistic for time scaled surveys in stratified sampling, Sci.Rep. 14 (1), 26700, 2024.
  • [26] P. V. Sukhatme and B. V. Sukhatme, Sampling theory of surveys with applications, 1970.
  • [27] P. Mukhopadhyay, Theory and methods of survey sampling, PHI Learning Pvt. Ltd., 2008.
There are 27 citations in total.

Details

Primary Language English
Subjects Theory of Sampling
Journal Section Statistics
Authors

Prayas Sharma 0000-0002-4828-1177

Mamta Kumari 0009-0001-8922-5374

Early Pub Date April 7, 2025
Publication Date April 28, 2025
Submission Date November 7, 2024
Acceptance Date March 27, 2025
Published in Issue Year 2025 Volume: 54 Issue: 2

Cite

APA Sharma, P., & Kumari, M. (2025). Variance estimation using Bernoulli auxiliary variable for time-scaled survey. Hacettepe Journal of Mathematics and Statistics, 54(2), 779-796. https://doi.org/10.15672/hujms.1580875
AMA Sharma P, Kumari M. Variance estimation using Bernoulli auxiliary variable for time-scaled survey. Hacettepe Journal of Mathematics and Statistics. April 2025;54(2):779-796. doi:10.15672/hujms.1580875
Chicago Sharma, Prayas, and Mamta Kumari. “Variance Estimation Using Bernoulli Auxiliary Variable for Time-Scaled Survey”. Hacettepe Journal of Mathematics and Statistics 54, no. 2 (April 2025): 779-96. https://doi.org/10.15672/hujms.1580875.
EndNote Sharma P, Kumari M (April 1, 2025) Variance estimation using Bernoulli auxiliary variable for time-scaled survey. Hacettepe Journal of Mathematics and Statistics 54 2 779–796.
IEEE P. Sharma and M. Kumari, “Variance estimation using Bernoulli auxiliary variable for time-scaled survey”, Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 2, pp. 779–796, 2025, doi: 10.15672/hujms.1580875.
ISNAD Sharma, Prayas - Kumari, Mamta. “Variance Estimation Using Bernoulli Auxiliary Variable for Time-Scaled Survey”. Hacettepe Journal of Mathematics and Statistics 54/2 (April 2025), 779-796. https://doi.org/10.15672/hujms.1580875.
JAMA Sharma P, Kumari M. Variance estimation using Bernoulli auxiliary variable for time-scaled survey. Hacettepe Journal of Mathematics and Statistics. 2025;54:779–796.
MLA Sharma, Prayas and Mamta Kumari. “Variance Estimation Using Bernoulli Auxiliary Variable for Time-Scaled Survey”. Hacettepe Journal of Mathematics and Statistics, vol. 54, no. 2, 2025, pp. 779-96, doi:10.15672/hujms.1580875.
Vancouver Sharma P, Kumari M. Variance estimation using Bernoulli auxiliary variable for time-scaled survey. Hacettepe Journal of Mathematics and Statistics. 2025;54(2):779-96.

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