Communications of the Korean Statistical Society 2011, Vol. 18, No. 2, 155–164 DOI: 10.5351/CKSS.2011.18.2.155 Ratio-Cum-Product Estimators of Population Mean Using Known Population Parameters of Auxiliary Variates Rajesh Tailor a , Rajesh Parmar a , Jong-Min Kim 1, b , Ritesh Tailor c a School of Studies in Statistics, Vikram University b Statistics, Division of Science and Mathematics, University of Minnesota-Morris c Institute of Would Science and Technology Abstract This paper suggests two ratio-cum-product estimators of finite population mean using known coefficient of variation and co-efficient of kurtosis of auxiliary characters. The bias and mean squared error of the proposed estimators with large sample approximation are derived. It has been shown that the estimators suggested by Upadhyaya and Singh (1999) are particular case of the suggested estimators. Almost ratio-cum product estimators of suggested estimators have also been obtained using Jackknife technique given by Quenouille (1956). An empirical study is also carried out to demonstrate the performance of the suggested estimators. Keywords: Ratio-cum-product estimator, population mean, coefficient of variation, coefficient of kurtosis, bias, mean squared error. 1. Introduction Use of auxiliary information has been in practice to increase the efficiency of the estimators. When the population mean of an auxiliary variate is known, so many estimators for population parameter( s) of study variate have been discussed in the literature. When correlation between study variate and auxiliary variate is positive (high) ratio method of estimation (Cochran, 1940) is used. On the other hand if the correlation is negative, product method of estimation (Robson, 1957; Murthy, 1967) is preferred. In practice information on coefficient of variation(CV) of an auxiliary variate is seldom known. Sisodia and Dwivedi (1981) suggested a modified ratio estimator for population mean of the study variate. Later on Upadhyaya and Singh (1999), derived another ratio and product type estimators using coefficient of variation and coefficient of kurtosis of the auxiliary variate. Singh (1967) utilized information on two auxiliary variates x 1 and x 2 and suggested a ratio-cum-product estimator for population mean. Singh and Tailor (2005) utilized known correlation coefficient between auxiliary variates (ρ x 1 x 2 ) x 1 and x 2 . Singh and Tailor (2005) motivates authors to suggest ratio-cum-product estimators of population mean utilizing the information on co-efficient of variation of auxiliary variates i.e. C x 1 and C x 2 and co-efficient of kurtosis of auxiliary variates β 2 ( x 1 ) and β 2 ( x 2 ) besides the population means ( ¯ X 1 and ¯ X 2 ) of auxiliary variates x 1 and x 2 . Let U = {U 1 , U 2 ,..., U N } be a finite population of N units. Suppose two auxiliary variates x 1 and x 2 are observed on U i (i = 1, 2,..., N), where x 1 is positively and x 2 is negatively correlated with the study variate y. A simple random sample of size n with n < N, is drawn using simple random sampling without replacement(SRSWOR) from the population U to estimate the population mean( ¯ Y ) 1 Corresponding author: Associate Professor, Statistics, Division of Science and Mathematics, University of Minnesota- Morris, MN 5627, USA. E-mail: jongmink@morris.umn.edu