A modified class of exponential-type estimator of population-mean in simple random sampling

  • Authors

    • Ekaette Enang Department of Statistics, University of Calabar
    • Joy Uket Department of Statistics, University of Calabar
    • Emmanuel Ekpenyong Department of Statistics, Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria
    2017-06-27
    https://doi.org/10.14419/ijasp.v5i2.7345
  • Simple Random Sampling, Auxiliary Information, Exponential Ratio Estimator, Mean Square Error, Optimality Conditions, Efficiency.

  • Abstract

    The problem of obtaining better ratio estimators of the population means are dominating in survey sampling. This paper provides a modified class of exponential type estimators using combinations of some existing estimators. Expressions for the bias and Mean Square Error (MSE) with the optimality conditions for this class of estimators have been established. Both analytical and numerical comparison with some existing estimators shows better performances from members of the proposed class.

  • References

    1. [1] Bahl, S. & Tuteja, R. K. (1991). Ratio and product type exponential estimator. Information and Optimization Sciences, 7(1), 159-163. https://doi.org/10.1080/02522667.1991.10699058.

      [2] Choudhury, S, & Singh, B, K. (2013). A class of product-cum-dual to product estimators of the population mean in survey sampling using auxiliary information. Asian Journal of Mathematics and Statistics, 6 (1), 1-11. https://doi.org/10.3923/ajms.2013.1.11.

      [3] Choudhury, S. & Singh, B, K. (2012). An efficient class of dual to product-cum-dual to ratio estimators of finite population mean in sample surveys. Global Journal of Science Frontier Research, Mathematics and Decision Sciences, 12 (3), 25-33.

      [4] Cochran, W. G. (1940). The estimation of the yields of the general experiments by sampling for the ratio of grain to total produce. Journal of Agricultural Sciences, 30(1), 262-275. https://doi.org/10.1017/S0021859600048012.

      [5] Das, A. K. (1988). Contribution to the theory of sampling strategies based on auxiliary information. Ph.D thesis submitted to Bidhan Chandra, India

      [6] Enang, E. I., Akpan, V. M. & Ekpenyong, E. J. (2014). Alternative ratio estimator of population mean in simple random sampling. Journal of Mathematical Research, 6(3), 54-61. https://doi.org/10.5539/jmr.v6n3p54.

      [7] Jhajj, H. S., Sharma, M. K., & Grover, L. K. (2005). An efficient class of chain estimators of population variance under sub-sampling scheme. Journal of the Japan Statistical Society, 35(2), 273-286. https://doi.org/10.14490/jjss.35.273.

      [8] Kadilar, C. & Cingi, H. (2003). A study on the chain ratio-types estimator. Hencettepe Journal of Mathematics and Statistics, 32, 105-108.

      [9] Kadilar, C. & Cingi, H. (2004). Ratio estimation in simple random sampling. Applied Journal of Mathematics and Computation. 151, 893-902. https://doi.org/10.1016/S0096-3003(03)00803-8.

      [10] Kadilar, C. & Cingi, H. (2006) Improvement in estimating the population mean in simple random sampling. Applied Mathematics Letters, 19(1), 75-79. https://doi.org/10.1016/j.aml.2005.02.039.

      [11] Mohanty, S. & Das, M. N. (1971). Use of transformation in sampling. Journal of the Indian Society of Agricultural Statistics, 23(1), 83-87.

      [12] Murthy, M. N. (1964). Product method of estimation. Sankhya: The Indian Journal of Statistics, Series A, 26(1), 69-74.

      [13] Okafor, F. C. (2002). Sample Survey Theory with Applications. 1st Edition. Afro-Orbis publishers, Nsukka Nigeria.

      [14] Robson, D. S. (1957). Applications of multivariate polykays to the theory of unbiased ratio- type estimation. Journal of American Statistical Association, 52, 511-522. https://doi.org/10.1080/01621459.1957.10501407.

      [15] Sharma, B. & Tailor, R. (2010). 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.

      [16] Singh, B. K., Choudhury, S. & Kumar, A. (2013). Improved exponential product cum dual to product type estimator of population mean. American Institute of Physics Conference Proceedings, 1557(1), 478-481. https://doi.org/10.1063/1.4823960.

      [17] Singh, H. P. & Espejo, M. R. (2003). On linear regression and ratio-product estimation of a finite population mean. Journal of the Royal Statistical Society, Series D, 52(1), 59-67. https://doi.org/10.1111/1467-9884.00341.

      [18] Singh, H. P. & Rathour, A. & Solanki, R. S., (2012). An improved dual to chain ratio type estimator for the population mean. Journal of Statistics, 1 (3), 1-6.

      [19] Singh, H. P. & Tailor, R. (2005). Estimation of finite population mean using known correlation coefficient between auxiliary characters statistics, Statistica, anno LXV, 4, 407-418.

      [20] Tailor R. & Sharma, B. K. (2009). A modified ratio-cum-product estimator of finite population mean using known coefficient of variation and coefficient of kurtosis. Statistics in Transition- New Series, 10 (1), 15-24.

      [21] Upadhyaya, L. N. & Singh, H. P. (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical Journal, 41(5), 627-636. https://doi.org/10.1002/(SICI)1521-4036(199909)41:5<627::AID-BIMJ627>3.0.CO;2-W.

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  • Received date: 2017-02-11

    Accepted date: 2017-05-04

    Published date: 2017-06-27