Improving Efficiencies of Ratio- and Product-type Estimators for Estimating Population Mean for Time-based Survey
Statisticians often use auxiliary information at an estimation stage to increase efficiencies of estimators. In this article, we suggest modified ratio- and product-type estimators utilizing the known value of the coefficient of variation of the auxiliary variable for a time-based survey. Further, to excel the performance of the suggested estimators, we utilize information from the past surveys along with the current surveys through hybrid exponentially weighted average. We obtain expressions for biases and mean square errors of the suggested estimators. The conditions, under which the suggested estimators have less mean square errors than that of other existing estimators, are also obtained. The results obtained through an empirical analysis examine the use of information from past surveys along with current surveys and show that the mean square errors and biases of the suggested estimators are less than that of the existing estimators. For example: for a sample size 5, mean square error and bias of the suggested ratio-type estimator are (0.0414,0.0065) which are less than (0.5581,0.0944) of the existing Cochran (1940) estimator, (0.4788,0.0758), of Sisodia and Dwivedi (1981) estimator and (0.0482,0.0082) of Muhammad Noor-ul-Amin (2020) estimator. Similarly, mean square error and bias of the suggested product- type estimator are (0.0025,−0.0006) which are less than (0.0612,−0.0096) of the existing Murthy (1964) estimator, (0.0286,−0.0071), of Pandey and Dubey (1988) estimator and (0.0053,−0.0008) of Muhammad Noor-ul-Amin (2020) estimator.
Ahuja, T.K., P. Misra and O.K. Behwal. (2021). A generalized two phase sampling estimator of ratio of population means using auxiliary information. Journal of Reliability and Statistical Studies, 14(1), 1–16.
Aslam, I., M. Noor-ul-Amin, M. Hanif, and P. Sharma (2021). Memory type ratio and product estimators under ranked-based sampling schemes. Communications in Statistics-Theory and Methods, 1–23. https://doi.org/10.1080/03610926.2021.1924784
Aslam, I., M. Noor-ul-Amin, U. Yasmeen, M. Hanif (2020). Memory type ratio and product estimators in stratified sampling. Journal of Reliability and Statistical Studies, 13(1), 1–20. https://doi.org/10.13052/jrss0974-8024.1311
Cochran, W.G. (1940). The estimation of the yields of cereal experiments by sampling for the ratio of grain to total produce. The journal of Agricultural Science, 30(2), 262–275. https://doi.org/10.1017/S0021859600048012
Gujarati, D.N. (2003). Basic Econometrics, McGraw-Hill. New York, IV edition.
Haq, A. (2013). A new hybrid exponentially weighted moving average control chart for monitoring process mean. Quality and Reliability Engineering International, 29(7), 1015–1025. https://doi.org/10.1002/qre.1453
Haq, A. (2017). A new hybrid exponentially weighted moving average control chart for monitoring process mean: discussion. Quality and Reliability Engineering International, 33(7), 1629–1631. https://doi.org/10.1002/qre.2092
Kumar, K., S. Kumar. (2020). Two phase sampling exponential type estimators for population mean using auxiliary attribute in the presence of non-response. International Journal of Mathematics and Statistics, 21(1), 75–85.
Maddala, G.S. (1992). Introduction to Econometrics, New York: Macmillan, II edition.
Mendenhall, W.M., T.L. Sincich (1992). Statistics for Engineering and the Sciences, New York, Dellen, III edition.
Misra, P. (2018). Regression type double sampling estimator of population mean using auxiliary information. Journal of Reliability and Statistical Studies, 11(1), 21–28.
Muhammad, I., J. Maria, L. Zhengyan (2019). Enhanced estimation of population mean in the presence of auxiliary information, Journal of King Saud University – Science, 31(4), 1373–1378.
Murthy, M.N. (1964). Product method of estimation. Sankhya: The Indian Journal of Statistics, Series A, 26(1), 69–74.
Noor-ul-Amin, M. (2020). Memory type ratio and product estimators for population mean for time-based surveys. Journal of Statistical Computation and Simulation, 90(17), 3080–3092. https://doi.org/10.1080/00949655.2020.1795660
Noor-ul-Amin, M. (2021). Memory type estimators of population mean using exponentially weighted moving averages for time scaled surveys. Communications in Statistics-Theory and Methods, 50(12), 2747–2758. https://doi.org/10.1080/03610926.2019.1670850
Pandey, B.N., V. Dubey (1988). Modified product estimator using coefficient of variation of auxiliary variate. Assam Stat Rev, 2, 64–66.
Singh, H.P., R.S. Solanki (2012). An alternative procedure for estimating the population mean in simple random sampling. Pakistan Journal of Statistics and Operation Research, 8(2), 213–232. https://doi.org/10.18187/pjsor.v8i2.252
Sisodia, B.V.S., V.K. Dwivedi (1981). A modified ratio estimator using coefficient of variation of auxiliary variable. J Indian Soc Agric Stat, New Delhi, 33, 13–18.