{"title":"New Product-Type Estimators for the Population Mean Using Quartiles of the Auxiliary Variable","authors":"Amer Ibrahim Falah Al-Omari","volume":25,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":16,"pagesEnd":21,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/6014","abstract":"

In this paper, we suggest new product-type estimators for the population mean of the variable of interest exploiting the first or the third quartile of the auxiliary variable. We obtain mean square error equations and the bias for the estimators. We study the properties of these estimators using simple random sampling (SRS) and ranked set sampling (RSS) methods. It is found that, SRS and RSS produce approximately unbiased estimators of the population mean. However, the RSS estimators are more efficient than those obtained using SRS based on the same number of measured units for all values of the correlation coefficient.<\/p>\r\n","references":" Cochran, W.G. (1977). Sampling Technique. 3rd edition, Wiley and\r\nSons. New York.\r\n Jemain, A. A. and Al-Omari, A. I. (2006). Multistage median ranked set\r\nsamples for estimating the population mean, Pakistan Journal of\r\nStatistics, 22(3): 195-207.\r\n McIntyre, G. A. (1952). A method for unbiased selective sampling using\r\nranked sets, Australian Journal of Agricultural Research. 3: 385-390.\r\n Muttlak, H. A., (1997). Median ranked set sampling, Journal of Applied\r\nStatistical Sciences. 6(4): 245-255.\r\n Pandey, B.N. and Dubey, V. (1998). Modified product estimator using\r\ncoefficient of variation of auxiliary variable, Assam Statistical Rev.,\r\n2(2): 64-66.\r\n Samawi. H. M. and Muttlak, H. A. (1996). Estimation of ratio using rank\r\nset sampling. The Biometrical Journal. 36(6): 753-764.\r\n Singh, H. P. and Tailor, R. (2003). Use of known correlation coefficient\r\nin estimating the finite population mean. Statistics in Transition. 6 (4):\r\n555-560.\r\n Takahasi K. and Wakimoto, K. (1968). On unbiased estimates of the\r\npopulation mean based on the sample stratified by means of ordering.\r\nAnnals of the Institute of Statistical Mathematics 20: 1-31.\r\n Upadhyaya, L.N. and Singh, H.P. (1999). Use of transformed auxiliary\r\nvariable in estimating the finite population mean. Biometrical Journal,\r\n41(5): 627-636.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 25, 2009"}