Improved Modified Class of Estimators in Estimating the Population Mean


  • Napattchan Dansawad Department of Applied Mathematics, Faculty of Science and Technology, Valaya Alongkorn Rajabhat University under the Royal Patronage, Phathum Thani


ratio type estimation, product type estimation, supplementary variable, bias, population mean


In this present paper, following the work of Yadav et al. [1], the author creates alternative class of estimators for estimating the population mean in situation of positive and negative correlations between supplementary and interested variables under simple random sampling without replacement (SRSWOR) scheme. Furthermore, this paper also introduces a modified class of estimators based on combination of alternative class of estimators and unbiased estimator. The expressions for the bias, Mean square error (MSE), and Minimum mean square error (MMSE) of all introduced estimators were considered. Both theoretical and numerical analysis were encouraging and supporting the performance of all introduced estimators for the mean estimation. The MSE and Percent relative efficiencies (PREs) were used as criteria for efficiency comparison between the new estimators and other existing estimators.


Download data is not yet available.


Yadav SK, Dixit MK, Dungana HN, Mishra SS. Improved estimators for estimating average yield using supplementary variable. Int J Math Eng Manag Sci 2019;4(5):1228-38.

Cochran WG. Sampling Techniques. 3rd ed. New York, John Wiley & Sons; 1977.

Robson DS. Application of multivariate polykays to the theory of unbiased ratio-type estimation. J Am Stat Assoc 1957;52(280):511-22.

Murthy MN. Product method of estimation. Sankhya, Series A, 1964;26(1):69-74.

Sisodia BVS, Dwivedi VK. A modified ratio estimator using coefficient of variation of supplementary variable. Jour Ind Soc Ag Statistics 1981;33(2):13-8.

Upadhyaya LN, Singh HP. Use of transformed auxiliary variable in estimating the finite population mean. Biom J 1999;41(5):627-36.

Singh HP, Tailor R, Kakaran MS. An estimator of population mean using power transformation. Jour Ind Soc Ag Statistics 2004;58(2):223-30.

Kadilar C, Cingi H. An Improvement in estimating the population mean by using the correlation coefficient. Hacet J Math Stat 2006;35(1):103-9.

Singh HP, Tailor R. Use of known correlation coefficient in estimating the finite population mean. SiT 2003;6(4):555-60.

Kadilar C, Cingi H. Ratio estimators in simple random sampling. Appl Math Comput 2004;151(3):893-902.

Ray SK, Singh RK. Difference-cum-ratio type estimators. J Ind Stat Assoc 1981; 19(24):147-51.

Al-Omari AI, Jemain AA, Ibrahim K. New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Investig Oper 2009;30(2):97-108.

Koyuncu N, Kadilar C. Efficient estimators for the population mean. Hacet J Math Stat 2009;38(2):217-25.

Yan Z, Tian B. Ratio method to the mean estimation using coefficient of skewness of supplementary variable. Info Com App 2010;106:103-10.

Subramani J, Kumarapandiyan G. Estimation of population mean using co-efficient of variation and median of an auxiliary variable. Int J Probab Stat 2012;1(4):111-8.

Jeelani MI, Maqbool S. Modified ratio estimators of population mean using linear combination of co-efficient of skewness and quartile deviation. South Pac J Nat Appl Sci 2013;31(1):39-44.

Jerajuddin M, Kishun J. Modified ratio estimators for population mean using size of the sample, selected from population. Int J Sci Res Sci Eng Technol 2016;2(2):10-6.

Pandey BN, Dubey V. Modified product estimator using coefficient of variation of supplementary variate. Assam Stat Rev 1988;2(2):64-6.

Singh GN. On the improvement of product method of estimation in sample surveys. Jour Ind Soc Ag Statistics 2003;56(3):267-75.

Yadav SK, Kadilar C. Improved class of ratio and product estimators. Appl Math Comput 2013;219(22):10726-31.

Khoshnevisan M, Singh R, Chauhan P, Sawan N, Smarandache F. A general family of estimators for estimating population mean using known value of some population parameter(s). Far East J Theor Stat 2007; 22(2):181-91.

Dobson J. An Introduction to Generalized Linear Models. 2nd ed. London, Chapman & Hall/CRC; 2002.