Abstract
Objectives: To estimate the finite populations mean using two auxiliary variables in double sampling as well as the efficiency of the proposed class of estimators. Methods: The mixing of estimators became more popular in developing more efficient estimators for estimating finite population parameters but while mixing two or more estimators, we should consider the basic purpose and the conditions under which the individual estimators are developed and are efficient. This paper deals with a class of mixed estimators of population mean by mixing ratio estimator and dual to product estimator in two phase sampling scheme using SRSWOR scheme to select the sample units at both the cases, i.e. Case-I: When X is unknown but Z is known and Case-II: When both X and Z are unknown. The purpose of mixing these two estimators is that both these estimators are designed to be used effectively for population mean when the population correlation coefficient between the study variable and the auxiliary variable is highly positive. Results: We observe that the proposed class of estimators is more efficient than the existing estimators which are available in literature and the empirical study indicates that the proposed class of estimators t01 and t02 performs better than the other existing estimators of t ′ 1; t ′ 2; t ′ 3; t ′ 4; t ′ 5; t ′ 6; t ′ 7; t ′ 8 and t ′ 9. Novelty: The percent relative efficiency (PRE) of the proposed class of estimators in Case-II i.e., t02 is superior than the estimator proposed in Case-I t01 for all the populations except Population 1 and 10, which needs further rigorous attention to compare the performances of t01 and t02: Keywords: Double sampling; Class of estimators; Bias; Mean square error (MSE); Percent relative efficiency (PRE)
Highlights
In sample survey literature, estimation of finite population parameters with a greater accuracy has become a matter of concern among the researchers for a long decade
We proposed a class of estimators for estimating the finite population mean by mixing of ratio and dual to product estimators in double sampling scheme
These two estimators which are mixed were designed to be used in case of positive correlation coefficient between the study variable y and the auxiliary variables x and z
Summary
Estimation of finite population parameters with a greater accuracy has become a matter of concern among the researchers for a long decade. (22) proposed novel estimators by adding an exponential parameter on the auxiliary variable.(23) proposed new class of exponential-type estimators in simple random sampling for the estimation of the population mean of the study variable using information of the population proportion possessing certain attributes. We draw another sample of size n(< n′ ) from the selected first phase sample usually known as the second phase sample s to observe the study variable y only At this stage, we are avoiding the case when both the samples are selected independently and directly from the population as the cases are very much similar to this case in the sense that the performance of our proposed class of estimators is like for both the cases. We extend our proposed class of estimators under these two cases as follows:
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
