Estimation of finite population mean in two-phase sampling with known coefficient of variation of an auxiliary character


  • Housila P. Singh Vikram University, Ujjain
  • Ritesh Tailor Institute of Wood Science and Technology, Bangalore
  • Rajesh Tailor Vikram University, Ujjain



In this paper a double (or two-phase) sampling version of (Singh and Tailor, 2005) estimator has been suggested along with its properties under large sample approximation. It is shown that the estimator due to (Kawathekar and Ajgaonkar, 1984) is a member of the proposed class of estimators. Realistic conditions have been obtained under which the proposed estimator is better than usual unbiased estimator, usual double sampling ratio ( tRd ) product ( tPd ) estimators and (Kawathekar and Ajgaonkar, 1984) estimator. This fact has been shown also through an empirical study.


A.K. DAS (1988), Contribution to the theory of sampling strategies based on auxiliary information. Ph.D. thesis submitted to BCKV; Mohanpur Nadia West Bengal India.

A.K. DAS, T.P. TRIPATHI (1978), Use of auxiliary information in estimating the finite population variance. “Sankhya” C 40, pp. 139-148.

D. ADHVARYU, GUPTA P.C. (1983), On some alternative strategies using auxiliary information. “Metrika” 30, pp. 217-226.

D.M. KAWATHEKAR, S.G.P AJAGAONKAR (1984), A modified ratio estimator based on the coefficient of variation in double sampling. “Journal of Indian Statistical Association.” 36 (2) pp. 47-50.

G.S. MADDALA (1977), Econometrics “McGraw Hills pub.Co.” New York.

H. P. SINGH, L.N. UPADHYAYA (1986), A dual to modified ratio estimator using coefficient of variation of auxiliary variable. “Proceedings National Academy of Sciences” (India) 56, A IV, pp. 336-340.

H.P. SINGH (1986), A generalized class of estimators of ratio product and mean using supplementary information on an auxiliary character in PPSWR sampling scheme.“Gujarat Statistical Review” 13(2), pp. 1-30.

H.P. SINGH, L.N. UPADHYAYA, P. CHANDRA (2004), A general family of estimators for estimating population mean using two auxiliary variables in two-phase sampling. “Statistics in Transition” 6 (7), pp. 1055-1077.

H.P. SINGH, M.R. ESPEJO (2003), On linear regression and ratio – product estimation of a finite population mean. “Statistician” 52(1), pp. 59-67.

H.P. SINGH, R. TAILOR (2005), Estimation of finite population mean with coefficient of variation of an auxiliary character. “Statistica” 65 (3), pp. 407-413.

M.N. MURTHY (1967), Sampling theory and methods Statistical Publishing Society Calcutta (India), pp. 1-1220 (Vol. I and Vol. II) Kluwer Academic Publishers The Netherlands.

R.G.D. STEEL, J. H. TORRIE (1960), Principles and procedures of Statistics McGraw Hill Book Co.

S. SINGH (2003), Advanced sampling theory with applications, How Michel “Selected Amy.

S.K. SRIVASTAVA (1970), A two phase sampling estimator in sample surveys. “Australian Journal of Statistics”, 12, pp. 23-27.

V. N. REDDY (1978), A study on the use of prior knowledge on certain population parameters in estimation. “Sankhya” C, 40, pp. 29-37.




How to Cite

Singh, H. P., Tailor, R., & Tailor, R. (2012). Estimation of finite population mean in two-phase sampling with known coefficient of variation of an auxiliary character. Statistica, 72(1), 111–126.