Almost Unbiased Estimators for Population Coefficient of Variation Using Auxiliary Information

Rajesh Singh

Department of Statistics, Institute of science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India.

Rohan Mishra

Department of Statistics, Institute of science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India.

Anamika Kumari

Department of Statistics, Institute of science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India.

Sunil Kumar Yadav *

Department of Statistics, Institute of science, Banaras Hindu University, Varanasi-221005, Uttar Pradesh, India.

*Author to whom correspondence should be addressed.


Abstract

The objective of the paper is to propose an almost unbiased ratio estimator for the finite coefficient of variation (CV). In this paper, we have proposed an exponential ratio type and log ratio type estimators for estimating population coefficient of variation. Two real data sets and one simulation study is carried out in support of the theoretical results. Mean squared error and Percent relative efficiency criteria is used to assess the performance of the estimators. It has been shown that the proposed class of estimators are almost unbiased up to the first order of approximation. Also proposed estimators are better in efficiency to other estimators consider in this study.

Keywords: Auxiliary information, bias, mean squared error, coefficient of variation, log type estimator


How to Cite

Singh , R., Mishra , R., Kumari , A., & Yadav , S. K. (2024). Almost Unbiased Estimators for Population Coefficient of Variation Using Auxiliary Information. Asian Journal of Probability and Statistics, 26(5), 1–18. https://doi.org/10.9734/ajpas/2024/v26i5614

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References

Cochran WG. Sampling techniques. John Wiley and Sons; 1977 Available:https://books.google.com/books?hl=en&lr=&id=xbNn41DUrNwC&oi=fnd&pg=PA1&dq=Sampling+Techniques+Book+by+William+Cochran&ots=TYrUiAwmkZ&sig=V1VYvy7LsjGVVBuUtFfbRsczbOo

Cochran WG. The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. J. Agric. Sci. 1940;30(2):262–275.

Robson DS. Applications of multivariate Polykays to the theory of unbiased ratio-type estimation. J. Am. Stat. Assoc. 1957;52(280):511–522. DOI: 10.1080/01621459.1957.10501407

Murthy MN. Product method of estimation. Sankhyā Indian J. Stat. Ser. A. 1964;69–74.

Solanki RS, Singh HP, Rathour A. An alternative estimator for estimating the finite population mean using auxiliary information in sample surveys. ISRN Probab. Stat. 2012;2012:1–14 DOI: 10.5402/2012/657682

Ray SK, Sahai A. Efficient Families of Ratio and Product-Type Estimators. Biometrika; 1980.

Srivastava SK, Jhajj HS. A class of estimators of the population mean in survey sampling using auxiliary information. Biometrika; 1981

Singh R, Mishra M, Singh BP, Singh P, Adichwal NK. Improved estimators for population coefficient of variation using auxiliary variable. J. Stat. Manag. Syst. 2018;21(7):1335–1355 DOI: 10.1080/09720510.2018.1503405

Sing R, Kumar M. A note on transformations on auxiliary variable in survey sampling. Model Assist. Stat. Appl. 2011;6(1):17–19. DOI: 10.3233/MAS-2011-0154

Malik S, Singh R. An improved estimator using two auxiliary attributes. Appl. Math. Comput. 2013;219(23):10983–10986 DOI: 10.1016/j.amc.2013.05.014

Das AK, Tripathi TP. Use of auxiliary information in estimating the coefficient of variation. Alig J Stat. 1992;12:51–58.

Patel PA, Rina S. A Monte Carlo comparison of some suggested estimators of Co-efficient of variation in finite population. J. Stat. Sci. 2009;1(2):137–147.

Breunig R. An almost unbiased estimator of the coefficient of variation. Econ. Lett. 2001;70(1):15– 19. DOI: 10.1016/S0165-1765(00)00351-7

Rajyaguru A, Gupta PC. On the estimation of the coefficient of variation from finite population-II. Model Assist. Stat. Appl. 2005;1(1):57–66. DOI: 10.3233/MAS-2006-1110

Adejumobi A, Yunusa MA. Some improved class of ratio estimators for finite population variance with the use of known parameters. LC Int. J. STEM ISSN 2708-7123. 2022;3(3):35–45.

Yunusa MA, et al. Logarithmic ratio-type estimator of population coefficient of variation. Asian J. Probab. Stat. 2021;14(2):13–22.

Audu A, et al. Difference-cum-ratio estimators for estimating finite population coefficient of variation in simple random sampling. Asian J. Probab. Stat. 2021;13(3):13–29.

Archana V, Rao A. Some improved estimators of co-efficient of variation from bi-variate normal distribution: A Monte Carlo comparison. Pak. J. Stat. Oper. Res. 2014;87–105.

Murthy MN. Sampling theory and methods. Sampl. Theory Methods; 1967. Available:https://www.cabdirect.org/cabdirect/abstract/19702700466

Singh S. Advanced sampling theory with applications: How Michael selected Amy. Springer Science and Business Media. 2003;2. Available:https://books.google.com/books?hl=en&lr=&id=8XGDJFotX_QC&oi=fnd&pg=PA615&dq=SINGH,+S.,+(2003).+Advanced+Sampling+Theory+With+Applications:+How+Michael+Selected+Amy+(Vol.+2),+Springer+Science+and+Business+Media.&ots=2tdrEnZykt&sig=Fvsjf34tjMfw_pD-v4mVFDyJuE0