On some efficient classes of estimators using auxiliary attribute

Shashi Bhushan; Anoop Kumar

doi:10.59170/stattrans-2023-025

On some efficient classes of estimators using auxiliary attribute

Shashi Bhushan Department of Statistics, University of Lucknow, Lucknow, India, 226007 ORCID:https://orcid.org/0000-0002-3931-888X , Anoop Kumar Department of Statistics, Amity University, Lucknow, India ORCID:https://orcid.org/0000-0003-2775-6548 Statistics in Transition new series, vol. 24, 2023, 2, pages: 141-157 Published online: 15 March 2023 DOI 10.59170/stattrans-2023-025 Citation: Bhushan, S., Kumar, A., 2023. On some efficient classes of estimators using auxiliary attribute. Statistics in Transition new series, 24(2), pp. 141-157. https://doi.org/10.59170/stattrans-2023-025

515 Views 51 Downloads

ARTICLE

(English) PDF

ABSTRACT

This paper considers some efficient classes of estimators for the estimation of population mean using known population proportion. The usual mean estimator, classical ratio, and regression estimators suggested by Naik and Gupta (1996) and Abd-Elfattah et al. (2010) estimators are identified as the members of the suggested class of estimators. The expressions of bias and mean square errors are derived up to first-order approximation. The proposed estimators were put to test against various other competing estimators till date. It has been found both theoretically and empirically that the suggested classes of estimators dominate the existing estimators.

KEYWORDS

Bias, Mean square error, Efficiency, Auxiliary attribute.

REFERENCES

Abd-Elfattah, A.M., El-Sherpieny, E.A., Mohamed, S.M., Abdou, O.F., (2010). Improvement in estimating the population mean in simple random sampling using information on auxiliary attribute. Applied Mathematics and Computation, 215, pp. 4198–4202.

Bahl, S., Tuteja, R.K., (1991). Ratio and product type exponential estimator. Information and Optimization Sciences, 12, pp. 159–163.

Bhushan, S., Gupta, R., (2019). Some log-type classes of estimators using auxiliary attribute. Advances in Computational Sciences and Technology, 12(2), pp. 99–108.

Bhushan, S., Gupta, R., (2020). An improved log-type family of estimators using attribute. Journal of Statistics and Management Systems, 23(3), pp. 593–602.

Bhushan, S., Kumar, A., (2020). Log type estimators of population mean under ranked set sampling. Predictive Analytics using Statistics and Big Data: Concepts and Modeling, 28, pp. 47–74.

Bhushan, S., Kumar, A., (2022). On optimal classes of estimators under ranked set sampling. Communications in Statistics - Theory and Methods, 51(8), pp. 2610–2639.

Bhushan, S., Gupta, R., Singh, S., Kumar, A., (2020a). A modified class of log-type estimators for population mean using auxiliary information on variables. International Journal of Applied Engineering Research, 15(6), pp. 612–627.

Bhushan, S., Gupta, R., Singh, S., Kumar, A., (2020b). Some improved classes of estimators using auxiliary information. International Journal for Research in Applied Science & Engineering Technology, 8(VI), pp. 1088–1098.

Bhushan, S., Gupta, R., Singh, S., Kumar, A., (2020c). A new efficient log-type class of estimators using auxiliary variable. International Journal of Statistics and Systems, 15(1), pp. 19–28.

Bhushan, S., Gupta, R., Singh, S., Kumar, A., (2020d). Some new improved classes of estimators using multiple auxiliary information. Global Journal of Pure and Applied Mathematics, 16(3), pp. 515–528.

Bhushan, S., Gupta, R., Singh, S., Kumar, A., (2020e). Some log-type classes of estimators using multiple auxiliary information. International Journal of Scientific Engineering and Research, 8(6), pp. 12–17.

Bhushan, S., Kumar, A., Singh, S., (2021). Some efficient classes of estimators under stratified sampling. Communications in Statistics - Theory and Methods, pp. 1–30. DOI:https://doi.org/10.1080/03610926.2021.1939052.

Grover, L. K., Kaur, P., (2011). An improved exponential estimator of finite population mean in simple random sampling using an auxiliary attribute. Applied Mathematics and Computation, 218(7), pp. 3093–3099.

Hansen, M. H. Hurwitz,W. N., Madow,W. G., (1953). Sample Survey Methods and Theory. John Wiley and Sons, New York, U.S.A.

Jhajj, H. S., Sharma, M. K., Grover, L. K., (2006). A family of estimators of population mean using information on auxiliary attribute. Pakistan Journal of Statistics, 22, pp. 43–50.

Kadilar, C., Cingi, H., (2006). Improvement in estimating the population mean in simple random sampling. Applied Mathematics Letters, 19, pp. 75–79.

Koyuncu, N., (2012). Efficient estimators of population mean using auxiliary attributes. Applied Mathematics and Computation, 218(22), pp. 10900–10905.

Naik, V. D., Gupta, P.C., (1996). A note on estimation of mean with known population proportion of an auxiliary character. Journal of Indian Society of Agricultural Statistics, 48(2), pp. 151–158.

Ozel, K. G., (2016). A new exponential type estimator for the population mean in simple random sampling. Journal of Modern Applied Statistical Methods, 15(2), pp. 207– 214.

Solanki, R. S., Singh, H. P., (2013). Improved estimation of population mean using population proportion of an auxiliary character. Chilean Journal of Statistics, 4(1), pp. 3–17.

Singh, R., Chouhan, P., Sawan, N., Smarandache, F., (2007). Ratio-product type exponential estimator for estimating finite population mean using information on auxiliary attribute. Renaissance High Press, USA. pp. 18–32.

Singh, R., Chauhan, P., Sawan, N., Smarandache, F., (2008). Ratio estimators in simple random sampling using information on auxiliary attribute. Pakistan Journal of Statistics and Operation Research, IV(1), pp. 47–53.

Singh, H. P., Solanki, R. S., (2012). Improved estimation of population mean in simple random sampling using information on auxiliary attribute. Applied Mathematics and Computation, 218(15), pp. 7798–7812.

Srivastava, S. K., (1967). An estimator using auxiliary information. Calcutta Statistical Association Bulletin, 16, pp. 121–132.

Sukhatme, P. V., Sukhatme, B. V., (1970). Sampling Theory of Surveys with Applications. Iowa State University Press, Ames, U.S.A.

Walsh, J. E., (1970). Generalization of ratio estimator for population total. Sankhya, A, 32, pp. 99–106.

Yadav, S. K., Zaman, T., (2020). A general exponential family of estimators for population mean using auxiliary attribute. Journal of Science and Arts, 20(1), pp. 25–34.

Zaman, T., Saglam, V., Sagir, M., Yucesoy, E., Zobu, M., (2014). Investigation of some estimators via Taylor series approach and an application. American Journal of Theoretical and Applied Statistics, 3(5), pp. 141–147.

Zaman, T., Kadilar, C., (2019). Novel family of exponential estimators using information of auxiliary attribute. Journal of Statistics and Management Systems, 22(8), pp. 1499– 1509.

Zaman, T., Toksoy, E., (2019). Improvement in estimating the population mean in simple random sampling using information on two auxiliary attributes and numerical application in agricultural engineering. Fresenius Environmental Bulletin, 28(6), pp. 4584– 4590.

Zaman, T., (2019a). Improved estimators using coefficient of skewness of auxiliary attribute. Journal of Reliability and Statistical Studies, pp. 177–186.

Zaman, T., (2019b). Efficient estimators of population mean using auxiliary attribute in stratified random sampling. Advances and Applications in Statistics, 56(2), pp. 153– 171.

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

Zaman, T., Kadilar, C., (2020). On estimating the population mean using auxiliary character in stratified random sampling. Journal of Statistics and Management Systems, 23(8), pp. 1415–1426.

Zaman, T., (2021). An efficient exponential estimator of the mean under stratified random sampling. Mathematical Population Studies, 28(2), pp. 104–121.

Zaman, T., Kadilar, C., (2021a). Exponential ratio and product type estimators of the mean in stratified two-phase sampling. AIMS Mathematics, 6(5), pp. 4265–4279.

Zaman, T., Kadilar, C., (2021b). New class of exponential estimators for finite population mean in two-phase sampling. Communications in Statistics-Theory and Methods, 50(4), pp. 874–889.