# Matrix Science Mathematic (MSMK)

### CUM DUAL PRODUCT ESTIMATOR FOR THE POPULATION MEAN USING RANKED SET SAMPLING

October 18, 2022 Posted by Natasha In MSMK

## ABSTRACT

### CUM DUAL PRODUCT ESTIMATOR FOR THE POPULATION MEAN USING RANKED SET SAMPLING

Journal: Matrix Science Mathematic (MSMK)
Author: Raji Idowu, Ilugbo Stephen Olubusola, Owojori Adefope Adeyanju, Afolabi Habeeb Abiodun

This is an open access article distributed under the Creative Commons Attribution License CC BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited

It has been shown that Ranked Set Sampling (RSS) is highly beneficial to the estimation based on Simple Random Sampling (SRS). There has been considerable development and many modifications were done to this method. The problem of estimating the population means is an integral aspect of a scientific survey. The estimators were examined for cum-dual products under Ranked Set Sampling (RSS), while the first-order approximation to the bias and Mean Square Error (MSE) of the proposed estimators were obtained. The numerical illustration of the comparisons was carried out to support the claim that the proposed estimators are more efficient than some existing estimators. Data were simulated for study variable y and auxiliary variable x using R software for the analysis to support the claim. The result shows that MSE of the proposed estimators, y ̅_(pd,RSS)^* is smaller than the MSE of the existing estimators y ̅_pd^*,y ̅_Rd^*, y ̅_(R,RSS)^*,y ̅_(RSS,MM1)^* and y ̅_(RSS,MM2)^* and y ̅_(RSS,MM3)^* at ρ = −0.1,−0.2,0.1,0.2, hence, the proposed estimator performed better than the existing estimators. While the MSE of the proposed estimator yy ̅_(pd,RSS)^* is greater than the MSE of the existing estimators y ̅_pd^* and y ̅_Rd^* at ρ = -0.3 and 0.3. However, the proposed estimator y ̅_(pd,RSS)^* does not perform better than the estimators, y ̅_pd^*,and y ̅_Rd^* at ρ = -0.3 and 0.3. It was concluded that the proposed estimator was more efficient than a class of regression estimators and four existing ratio-type estimators based on RSS.
 Pages 26-29 Year 2022 Issue 1 Volume 6