# Modified Ratio-Cum-Product Estimators of Population Mean Using Two Auxiliary Variables

## Main Article Content

## Abstract

A percentile is one of the measures of location used by statisticians showing the value below which a given percentage of observations in a group of observations fall. A family of ratio-cum-product estimators for estimating the finite population mean of the study variable when the finite population mean of two auxiliary variables are known in simple random sampling without replacement (SRSWOR) have been proposed. The main purpose of this study is to develop new ratio-cum-product estimators in order to improve the precision of estimation of population mean in sample random sampling without replacement using information of percentiles with two auxiliary variables. The expressions of the bias and mean square error (MSE) of the proposed estimators were derived by Taylor series method up to first degree of approximation. The efficiency conditions under which the proposed ratio-cum-product estimators are better than sample man, ratio estimator, product estimator and other estimators considered in this study have been established. The numerical and empirical results show that the proposed estimators are more efficient than the sample mean, ratio estimator, product estimator and other existing estimators.

## Article Details

*Asian Journal of Research in Computer Science*,

*6*(1), 55-65. https://doi.org/10.9734/ajrcos/2020/v6i130152

## References

Upadhyaya LN, Singh HP. Use of Transformed Auxiliary Variable in Estimating the Finite Population Mean. Biometrical Journal. 1999;41:627–636.

Abu-Dayyeh WA, Ahmed MS, Ahmed RA, Muttlak HA. Some Estimators of a Finite Population Mean using Auxiliary Information, Applied Mathematics and Computation. 2003; 139:287–298.

Singh HP, Tailor R, Kakran MS. An Improved Estimation of Population Mean using Power Transformation. Journal of the Indian Society of Agricultural Statistics, 2004; 8(2):223–230.

Kadilar C, Cingi H. A new estimator using two auxiliary variables. Applied Mathematics and Computation. 2005; 162: 901–908.

Tailor R, Jatwa NK, Tailor R, Garg N. Dual to Ratio and Product Type Exponential Estimators in Stratified Random Sampling Using Two Auxiliary Variates, Journal of Reliability and Statistical Studies. 20136; 2: 115-126.

Jeelani MI, Maqbool S, Mir SA. Modified Ratio Estimators of Population Mean using Linear Combination of Estimators of Population Mean using Linear Combination of Coefficient of Skewness and Quartile Deviation. International Journal of Modern Mathematical Sciences. 2013; 6:174–183.

Gupta RK, Yadav SK. New Efficient Estimators of Population Mean Using Non-Traditional Measures of Dispersion. Open Journal of Statistics, 2017;7: 394-404.

Muili JO, Singh RVK, Audu A. Study of Efficiency of Some Finite Population Variance Estimators in Stratified Random Sampling. Continental Journal Applied Sciences. 2018; 13(2):1 – 17.

Muili JO, Audu A. Modification of Ratio Estimator for Population Mean. Annals. Computer Science Series. 2019:17(2):74-78.

Muili JO, Audu A, Singh RVK, Odeyale AB, Adebiyi A. Improved Variance Estimator Using Linear Combination of Tri-Mean and Quartile Average. Annals. Computer Science Series. 2019; 17(1):142-147.

Robson DS. Application of multivariate polykays to the theory of unbiased ratio-type estimation, Journal of the American Statistical Association, 1957; 52:511–522.

Murthy MN. Sampling Theory and Methods; Statistical Publishing Society, Calcutta. India; 1967.

Singh HP, Tailor R. Use of known Correlation Coefficient in Estimating the Finite Population Means; Statistics in Transition. 2003; 6(4):555-560.

Abid M, Abbas N, Nazir HZ, Lin Z. Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-conventional Location Parameters. Revista Colombiana de Estadistica. 2016; 39(1):63 –79.

Kadilar C, Cingi H. Ratio Estimators in Stratified Random Sampling, Biometrical Journal. 2003; 45(2):218-225.

Koyuncu N, Kadilar C. Family of Estimators of Population Mean Using Two Auxiliary Variables in Stratified Random Sampling, Communications in Statistics: Theory and Methods, 2009;38(14):2398-2417.

Yan Z, Tian B. Ratio Method to the Mean Estimation using Coefficient of Skewness of Auxiliary Variable. In: Information Computing and Applications. ICICA; 2010.

Subramani J, Kumarapandiyan G. Modified Ratio Estimators using known Median and Co-efficient of Kurtosis. American Journal of Mathematics and Statistics, 2012; 2:95–100.

DOI:https://doi.org/10.5923/j.ajms.20120204.05

Yadav SK, Mishra SS, Kadilar C, Shukla AK. Improved Dual to Ratio Cum Dual to Product Estimator in the Stratified Random Sampling, American Journal of Operational Research, 2015; 5(3):57-63.

Gupta RK, Yadav SK. Improved Estimation of Population Mean Using Information on Size of the Sample. American Journal of Mathematics and Statistics. 2018; 8(2):27-35.

Muili JO, Audu A, Singh RVK, Yunusa IA. Improved Estimators of Finite Population Variance Using Unknown Weight of Auxiliary Variable. Annals. Computer Science Series. 2019; 17(1):148-153.

Muili JO, Audu A, Singh RVK. Modified Estimator of Finite Population Variance in Simple Random Sampling. Journal of Science and Technology Research. 2019; 1(1):81-90.

Muili JO, Audu A, Odeyale AB, Olawoyin IO. Ratio Estimators for Estimating Population Mean Using Tri-mean, Median and Quartile Deviation of Auxiliary Variable. Journal of Science and Technology Research 2019; 1(1):91-102.

Muili JO, Zakari Y, Audu A. Modified Class of Estimator of Finite Population Variance. FUDMA Journal of Sciences (FJS). 2019; 3(4):67-78.

Audu A, Ishaq OO, Zakari Y, Wisdom DD, Muili JO, Ndatsu AM. Regression-cum-Exponential Ratio Imputation Class of Estimators of Population Mean in the Presence of Non-response. Science Forum (Journal of Pure and Applied Sciences) 2020; 20:58–63.

Available:http://dx.doi.org/10.5455/sf.71109

Audu A, Ishaq OO, Muili JO, Zakari Y, Ndatsu AM, Muhammad S. On the Efficiency of Imputation Estimators using Auxiliary Attribute. Continental J. Applied Sciences. 2020;15(1):1-13

DOI: 10.5281/zenodo.3721046

Muili JO, Adebiyi A, Agwamba EN. Improved Ratio Estimators for Estimating Population Mean Using Auxiliary Information. International Journal of Scientific and Research Publications. 2020; 10(5):937-945.

Available:http://dx.doi.org/10.29322/IJSRP.10.05.2020.p101111

Singh MP. Ratio-cum-product method of estimation, Metrika, 1967; 12:34–42.

Singh HP, Tailor R. Estimation of finite population mean using known Correlation co-efficient between auxiliary characters, Statistica. 2005; 65:407–418.

Tailor R, Parmar R, Kim JM, Tailor R. Ratio-Cum-Product Estimators of Population Mean using known Population Parameters of Auxiliary Variates, Communications of the Korean Statistical Society. 2011; 18(2):155–164.

DOI: 10.5351/CKSS.2011.18.2.155

Yadav SK, Subramani J, Mishra SS, Shukla AK. Improved Ratio-Cum- Product Estimators of Population Mean Using Known Population Parameters of Auxiliary Variables. American Journal of Operational Research. 2016;6(2):48- 54

DOI: 10.5923/j.ajor.20160602.03