Generalized factor-type exponential estimators of population mean in sample surveys

Vinay Kumar Yadav; Shakti Prasad; Subhash Kumar  Yadav

doi:10.5269/bspm.66504

Vinay Kumar Yadav M S Ramaiah University of Applied Sciences https://orcid.org/0000-0003-2221-5873
Shakti Prasad Department of Basic and Applied Science, National Institute of Technology Arunachal Pradesh https://orcid.org/0000-0002-7867-7586
Subhash Kumar Yadav Babasaheb Bhimrao Ambedkar University https://orcid.org/0000-0002-7181-8075

Resumo

The present article deals with a generalized class of estimators for estimating the population mean in sample surveys, employing various combinations of auxiliary variables and considering some values of characterizing constant alpha ranging from -1 to +1. The proposed estimator may be consider as an efficient extension to the work of Singh and Shukla (Metron, 45(1-2): 273-283, 1987), Bahl and Tuteja (Journal of information and optimization sciences, 12(1), 159-164, 1991) and Kadilar (Journal of Modern Applied Statistical Methods: Vol. 15 : Iss. 2 , Article 15, 2016). The sampling properties of the suggested estimators have been derived up to the first degree of large sample approximations. The suggested estimators are shown to have smaller mean squared errors than the existing exponential estimators considered in this paper. The percent relative efficiencies with respect to the usual mean estimator are calculated. An improvement has been shown over the existing exponential estimators through theoretical conditions as well as by a numerical and simulation study based on COVID-19 death in India.

Downloads

Não há dados estatísticos.

Biografia do Autor

Vinay Kumar Yadav, M S Ramaiah University of Applied Sciences

Department of Data Sciences and Analytics, School of Social Sciences

Subhash Kumar Yadav, Babasaheb Bhimrao Ambedkar University

Department of Statistics, School of Physical & Decision Sciences

Referências

Oncel Cekim, Hatice, Modified unbiased estimators for population variance: An application for COVID-19 deaths in Russia, Concurrency and Computation: Practice and Experience: e7169, (2022).

Cochran, W. G., The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. The journal of agricultural science, 30(2), 262-275, (1940).

Murthy, M. N., Product method of estimation. The Indian Journal of Statistics, Series A, 69-74, (1964).

Hartley, H. O., Ross, A. , Unbiased ratio estimators. Nature, 174(4423), 270-271, (1954)

Sisodia, B. and Dwivedi, V., Modified Ratio Estimator Using Coefficient of Variation of Auxiliary Variable. Journal-Indian Society of Agricultural Statistics, 33, 13-18, (1981).

Goodman, L. A., Hartley, H. O., The precision of unbiased ratio-type estimators. Journal of the American Statistical Association, 53(282), 491-508, (1958).

Yan, Zaizai, and Bing Tian, Ratio method to the mean estimation using coefficient of skewness of auxiliary variable. In International Conference on Information Computing and Applications, pp. 103-110. Springer, Berlin, Heidelberg, (2010).

Williams, W. H., The precision of some unbiased regression estimators. Biometrics, 19(2), 352-361, (1963).

Tin, M., Comparison of some ratio estimators. Journal of the American Statistical Association, 60(309), 294-307, (1965).

Srivastava, S. K., Product estimator. Journal of Indian Statistical Association, 4, 29-37, (1966).

Walsh, J. E., Generalization of ratio estimate for population total. Sankhya: The Indian Journal of Statistics, Series A, 99-106, (1970).

Srivenkataramana, T., Tracy, D. S., An alternative to ratio method in sample surveys. Annals of the Institute of Statistical Mathematics, 32(1), 111-120, (1980).

Vos, J. W. E., Mixing of direct, ratio, and product method estimators. Statistica Neerlandica, 34(4), 209-218 , (1980 ).

Srivenkataramana, T, A dual to ratio estimator in sample surveys. Biometrika, 67(1), 199-204, ( 1980).

Isaki, C. T., Variance estimation using auxiliary information. Journal of the American Statistical Association, 78(381), 117-123, (1983).

Singh, R. V. K., Singh, B. K., Study of a Class of Ratio Type Estimator under Polynomial Regression Model. Proceedings of Mathematical Society, (2007).

Zakari, Y., J. O. Muili, M. N. Tela, N. S. Danchadi, and A. Audu, Use of unknown weight to enhance ratio-type estimator in simple random sampling. Lapai Journal of Applied and Natural Sciences 5, no. 1 : 74-81, (2020).

Ahmad, Sohaib, Sardar Hussain, and Sohail Ahmad, Finite population distribution function estimation using auxiliary information under simple random sampling. Statistics, Computing and Interdisciplinary Research 3, no. 1 : 29-38, (2021).

Singh, H. P., Solanki, R. S., Singh, A. K., Predictive estimation of finite population mean using exponential estimators. Statistika: Statistics and Economy Journal, 94(1), 41-53, (2014).

Bahl, S., Tuteja, R., Ratio and product type exponential estimators. Journal of information and optimization sciences, 12(1), 159-164, (1991).

Sharma, B., 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).

Monika, S. and Kumar, A., Exponential Type Product Estimator for Finite Population Mean with Information on Auxiliary Attribute. An International Journal of Applications and Applied Mathematics, 10(1): 106 – 113, (2015).

Upadhyaya, L. N., Singh, H. P., Chatterjee, S., & Yadav, R., Improved ratio and product exponential type estimators. Journal of statistical theory and practice, 5(2), 285-302, (2011).

Solanki, R. S., Singh, H. P., Rathour, A., An alternative estimator for estimating the finite population mean using auxiliary information in sample surveys. International Scholarly Research Notices, (2012).

Ozel Kadilar, Gamze, A New Exponential Type Estimator for the Population Mean in Simple Random Sampling. Journal of Modern Applied Statistical Methods: Vol. 15 : Iss. 2 , Article 15, (2016).

Irfan, Muhammad, Maria Javed, and Zhengyan Lin, Enhanced estimation of population mean in the presence of auxiliary information. Journal of King Saud University-Science 31, no. 4 : 1373-1378, (2019).

Irfan, Muhammad, Maria Javed, and S. Haider Bhatti, Difference-type-exponential estimators based on dual auxiliary information under simple random sampling. Scientia Iranica 29, no. 1 : 343-354, (2022).

Zaman, Tolga, and Cem Kadilar, Novel family of exponential estimators using information of auxiliary attribute. Journal of Statistics and Management Systems 22, no. 8 : 1499-1509, (2019).

Zaman, T., Generalized exponential estimators for the finite population mean. Statistics in Transition new series, 21(1), 159-168, (2020).

Zaman, Tolga, Murat Sagir, and Mehmet S¸ahin, A new exponential estimators for analysis of COVID-19 risk. Concurrency and Computation: Practice and Experience 34.10 : e6806, (2022).

Shahzad, Usman, Nadia H. Al-Noor, Muhammad Hanif, and Irsa Sajjad, An exponential family of median based estimators for mean estimation with simple random sampling scheme. Communications in Statistics-Theory and Methods 50, no. 20 : 4890-4899, (2021).

Ahmad, Sohail, Muhammad Arslan, Aamna Khan, and Javid Shabbir, A generalized exponential-type estimator for population mean using auxiliary attributes. Plos one 16, no. 5 : e0246947, (2021).

Prasad, S., Some linear regression type ratio exponential estimators for estimating the population mean based on quartile deviation and deciles. Statistics in Transition, New Series, 21(5), 85 - 98, (2020).

Prasad, S., Yadav, V. K., Imputation of Missing Data Through Product Type Exponential Methods in Sampling Theory. Revista Colombiana de Estad´ıstica, 46(1), 111-127, (2023).

Zaman, T., Sagir, M., S¸ahin, M., A new exponential estimators for analysis of COVID-19 risk. Concurrency and Computation: Practice and Experience, 34(10), e6806, (2022).

Singh, H. P., Gupta, A., Tailor, R., Estimation of population mean using a difference-type exponential imputation method. Journal of Statistical Theory and Practice, 15, 1-43, (2021).

Audu, A., Danbaba, A., Ahmad, S. K., Musa, N., Shehu, A., Ndatsu, A. M., & Joseph, A. O., On The Efficiency of Almost Unbiased Mean Imputation When Population Mean of Auxiliary Variable is Unknown. Asian Journal of Probability and Statistics. 2021e, 15(4), 235-250, (2021).

Singh, R., Chauhan, P., Sawan, N., Smarandache, F., Improvement in estimating the population mean using exponential estimator in simple random sampling.Auxiliary Information and a priori Values in Construction of Improved Estimators, 33, (2007).

Singh, V. K., and Shukla, D., One parameter family of factor-type ratio estimator. Metron, 45(1-2): 273-283, (1987).

R Core Team, R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/, (2021).