Development of Efficient Estimation Technique for Population Mean in Two Phase Sampling Using Fuzzy Tools

Parichha, P.; Basu, K.; Bandyopadhyay, A.; Mukhopadhyay, P.

doi:10.1515/jamsi-2017-0006

Abstract

The present investigation deals with the problem of estimation of population mean in two-phase (double) sampling. Utilizing information on two auxiliary variables, one chain exponential ratio and regression type estimator has been proposed and its properties are studied under two different structures of twophase sampling. To make the estimator practicable, unbiased version of the proposed strategy has also been developed. The dominance of the suggested estimator over some contemporary estimators of population mean has been established through numerical illustrations carried over the data set of some natural population and artificially generated population. Categorization of the dominance ranges of the proposed estimation strategies are deployed through defuzzification tools, which are followed by suitable recommendations.

References

[1] ANDERSON, T. W., 1958, An Introduction to Multivariate Statistical Analysis. John Wiley & Sons, Inc. New York.
Search in Google Scholar Back to article
[2] BANDYOPADHYAY, A. AND SINGH, G. N., 2014, Predictive estimation of population mean in two-phase sampling. Communications in Statistics- Theory and Methods. DOI: 10.1080/03610926.2014.919396, (Article in Press).10.1080/03610926.2014.919396()
Open DOI Search in Google Scholar Back to article
[3] CHAND, L., 1975, Some ratio type estimators based on two or more auxiliary variables.Unpublished Ph. D. thesis. Iowa State University, Ames, Iowa (USA).
Search in Google Scholar Back to article
[4] CHOUDHURY, S. AND SINGH, B. K., 2012, A class of chain ratio-product type estimators with two auxiliary variables under double sampling scheme. Journal of the Korean Statistical Society, 41, 247-256.10.1016/j.jkss.2011.09.002
Open DOI Search in Google Scholar Back to article
[5] CHATTERJEE, A., SINGH, G. N., BANDYOPADHYAY, A. AND MUKHOPADHYAY, P. 2015, A General Procedure for Estimating Population Variance in Successive Sampling using Fuzzy Tools. Hacettepe Journal of Mathematics and Statistics. ISSN: 1303-5010. (S. C. I. E. indexed ) (Article in Press) DOI: 10.15672/HJMS.20151001416910.15672/HJMS.201510014169
Open DOI Search in Google Scholar Back to article
[6] COCHRAN, W. G., 1940, The estimation of the yields of cereal experiments by sampling for the ratio gain to total produce. J. Agric. Soc. 30, 262-275.10.1017/S0021859600048012
Open DOI Search in Google Scholar Back to article
[7] COCHRAN, W. G., 1977, Sampling Techniques. Wiley Eastern Limited, New Delhi, III, Edition.
Search in Google Scholar Back to article
[8] GUPTA, S. AND SHABBIR, J., 2007, On the use of transformed auxiliary variables in estimating population mean by using two auxiliary variables. Journal of Statistical Planning and Inference, 137, 1606 - 1611.10.1016/j.jspi.2006.09.008
Search in Google Scholar Back to article
[9] HANDIQUE, B. K., DAS, G., AND KALITA, M. C., 2011, Comparative studies on forest sampling techniques with satellite remote sensing inputs. Project Report, NESAC, pp. 12-40.
Search in Google Scholar Back to article
[10] KIREGYERA, B., 1980, A chain ratio type estimators in finite population double sampling using two auxiliary variables. Metrika. 17, 217-223.10.1007/BF01893599
Search in Google Scholar Back to article
[11] KIREGYERA, B., 1984, Regression type estimators using two auxiliary variables and the model of double sampling from finite populations. Metrika. 31, 215-226.10.1007/BF01915203
Open DOI Search in Google Scholar Back to article
[12] REDDY, V. N., 1978, A study on the use of prior knowledge on certain population parameters in estimation. Sankhya, Series C. 40, 29-37.
Search in Google Scholar Back to article
[13] SHUKLA, D., PATHAK, SAND THAKUR, N. S., 2012, Estimation of population mean using two auxiliary sources in sample surveys. Statistics in Transition, 13(1), 21-36.10.59170/stattrans-2012-002
Search in Google Scholar Back to article
[14] SINGH, S., JOARDER, A. H. AND TRACY, D. S., 2001, Median estimation using double sampling. Australian & New Zealand Journal of Statistics, 43(1), 33-46.10.1111/1467-842X.00153
Open DOI Search in Google Scholar Back to article
[15] SINGH, S. AND DEO, B., 2003, Imputation by power transformation. Statistical Papers, 4, 555-579.10.1007/BF02926010
Open DOI Search in Google Scholar Back to article
[16] SINGH, H. P. AND ESPEJO, M. R., 2007, Double sampling ratio-product estimator of a finite population mean in sampling surveys. Journal of Applied Statistics, 34(1), 71-85.10.1080/02664760600994562
Open DOI Search in Google Scholar Back to article
[17] SINGH, H. P. AND VISHWAKARMA, G. K., 2007, Modified Exponential Ratio and Product Estimators for Finite Population Mean in Double Sampling. Austrian journal of statistics, 36 (3), 217-22510.17713/ajs.v36i3.333
Search in Google Scholar Back to article
[18] SINGH, H. P., CHANDRA, P., JOARDER, A. H. AND SINGH, S., 2007, Family of estimators of mean, ratio and product of a finite population using random nonresponse. Test, 16, 565-597.10.1007/s11749-006-0020-z
Search in Google Scholar Back to article
[19] SRIVASTAVA, S. K., 1970, A two-phase sampling estimator in sample surveys. Australian Journal of Statistics. 12(1), 23-27.10.1111/j.1467-842X.1970.tb00109.x
Open DOI Search in Google Scholar Back to article
[20] SUKHATME, B., 1962, Some ratio-type estimators in two - phase sampling. Journals of the American Statistics Associations. 57, 628-632.10.1080/01621459.1962.10500551
Search in Google Scholar Back to article
[21] SUKHATME, P. V. AND SUKHATME, B. V., 1970, Sampling theory of surveys with applications. Asia Publishing House, India.
Search in Google Scholar Back to article
[22] TRACY, D. S., SINGH, H. P., AND SINGH, R., 1996, An alternative to the ratio-cum-product estimator in sample surveys. Journal of Statistical Planning and Inference. 53, 375- 387.10.1016/0378-3758(95)00136-0
Search in Google Scholar Back to article

Development of Efficient Estimation Technique for Population Mean in Two Phase Sampling Using Fuzzy Tools

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