Generalized Logarithmic Ratio and Product-Type Estimators in Simple Random Sampling (SRS)

Nikita ¹ , S. Malik²

1. Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana, India.
2. Department of Mathematics, Baba Mastnath University, Asthal Bohar, Rohtak, Haryana, India.

Section:Research Paper, Product Type: Journal-Paper
Vol.9 , Issue.6 , pp.56-60, Dec-2022

Online published on Dec 31, 2022

Copyright © Nikita, S. Malik . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
The present study deals with a modified logarithmic ratio and product-type estimators in simple random sampling (SRS). The bias and mean square error (MSE) expressions based on the proposed estimator were obtained up to the first order of approximation. The proposed logarithmic ratio and product-type estimators outperform the classic simple mean, ratio, and product-type estimators. Some numerical datasets are used to illustrate and validate the theoretical results.

Key-Words / Index Term :
Logarithmic ratio; Product-type estimators; Bias; Mean square error; Efficiency

References :
[1] S. Bahl and R.K. Tuteja, “Ratio and product-type exponential estimator”, Inf. Optim. Sci. Vol.12, Issue 1, pp. 159-163, 1991.
[2] B.S.V. Sisodia, & V.K. Dwivedi, “A modified ratio estimator using coefficient of variation of auxiliary variable”, Jour. Ind. Soc. Agr. Stat., Vol. 33, Issue 2, pp. 13-18, 1981.
[3] A.K. Das, & T.P. Tripathi, “Use of auxiliary information in estimating the coefficient of variation”. Alig. J. of Statist., Vol. 12, pp. 51-58, 1992.
[4] L.N. Upadhyaya, & H.P. Singh, “Use of transformed auxiliary variable in estimating the finite population mean”, Biometrical J., Vol. 41, pp. 27-36, 1999.
[5] H.P. Singh, & R. Tailor, (2005). “Estimation of finite population mean with known coefficient of variation of an auxiliary character”, Statistica, Vol. 65, Issue 3, pp. 301-313, 2005.
[6] C. Kadilar, & H. Cingi, “Ratio estimators in simple random sampling”, Appl. Math. Comput., Vol. 151, pp. 893-902, 2004.
[7] H.P. Singh, & R. Tailor, “Use of known correlation coefficient in estimating the finite population mean”, Statist. Trans., Vol. 6, pp. 555-560, 2003.
[8] H.P. Singh, & R.S. Solanki, “An efficient class of estimators for the population mean using auxiliary information in systematic sampling”. J. Stat. Theory Pract., Vol. 6, No. 2, pp. 274-285, 2012.
[9] S. Bahl, and S. Malik, “Generalised synthetic estimator using double sampling scheme and auxiliary information”; Mathematics Journal of interdisciplinary sciences, Vol. 4, pp. 15-21, 2015.
[10] A.C. Onyeka, C.H. Izunobi, & I.S. Iwueze, “Separate-type estimators for estimating population ratio in post-stratified sampling using variable transformation”, Open J. Stat., Vol. 5, pp.27-34, 2015.
[11] M. Saini, & A. Kumar, “Exponential type product estimator for finite population mean with information on auxiliary attribute”, Applications and Applied Mathematics: An International Journal, (AAM), Vol. 10, Issue 1, Article 7, pp.1-8, 2015.
[12] M. Madhulika, B.P. Singh, & R. Singh, “Estimation of population mean using two auxiliary variables in stratified random sampling” J. Reliab. Stat. Stud., Vol. 10, No. 1, pp. 59-68, 2017.
[13] R. Singh, M. Mishra, B.P. Singh, P. Singh, & N.K. Adichwal, “Improved estimators for population coefficient of variation using auxiliary variables” J. Stat. Manag. Syst., Vol. 21, Issue 7, pp. 1335-1335, 2018.
[14] Nikita & S. Malik, “Regression cum exponential type estimator of the population mean in double sampling” YMER., Vol. 21, No 10, pp. 701-707, 2022.
[15] C. Kumari, & R.K. Thakur, “An efficient log-type class of estimators using auxiliary information under double sampling” J. Stat. Appl. Pro., Vol. 10, Issue 1, pp. 197-202, 2021.
[16] R. Singh, & S. Rai, “Log-type estimators for estimating population mean in systematic sampling in the presence of non-response” J. Reliab. Stat. Stud., Vol. 12, Issue 1, pp. 105-115, 2019.
[17] S. Bhushan, A. Kumar, D. Tyagiand, & S. Singh, (2022). “On some improved classes of estimators under stratified sampling using attribute”, J. Reliab. Stat. Stud., Vol. 15, Issue 1, pp. 187-210, 2022.
[18] S. Bhushan, R. Gupta, S. Singh, & A. Kumar, “A modified class of log-type estimators for population mean using auxiliary information on variables”. Int. J. Appl. Eng. Res., Vol. 15, Issue 6, pp. 612-627, 2020.
[19] S. Bhushan, & R. Gupta, “An improved log-type family of estimators using attribute”, J. Stat. Manag. Syst., Vol. 23, Issue 3, pp. 593-602, 2022.
[20] Megha, & S. Malik, “Generalized composite regression with ratio and product estimators in double sampling”, International Journal of Scientific Research in Mathematical and Statistical Sciences, Vol. 9, Issue 2, pp 31-35, 2022.
[21] W.G. Cochran, “Sampling Techniques”, 3rd Edition, John Wiley & Sons, New York 1977.
[22] C. Kadilar, & H. Cingi, “Ratio estimators for the population variance in simple and stratified random sampling” Appl. Math. Comput., Vol. 173, pp. 1047-1059, 2006.
[23] R. Tailor & S. Chouhan, “Ratio-cum-product type exponential estimator of finite population mean in stratified random sampling”, Communications in statistics-Theory and methods, Vol. 43, Issue 2, pp. 343-354, 2013.