Abstract
In this paper, we propose an improved new class of exponential-ratio-type estimators for estimating the finite population mean using the conventional and the nonconventional measures of the auxiliary variable. Expressions for the bias and MSE are obtained under large sample approximation. Both simulation and numerical studies are conducted to validate the theoretical findings. Use of the conventional and the nonconventional measures of the auxiliary variable is very common in survey research, but we observe that this does not add much value in many of the estimators except for our proposed class of estimators.
Highlights
Many research papers have appeared in the literature where authors have used the conventional and the nonconventional measures of the auxiliary variable to enhance the efficiency of estimators
We have proposed a general class of exponential-ratio-type estimators for finite population mean in simple random sampling using the conventional and the nonconventional measures
We observed that the efficiency of the estimators Y(j), (j S2, GK, YK, Ia, Ib) in some situations does not increase much as compared to other estimators. e percent relative efficiency (PRE) of Irfan et al.’s estimator [11] was undefined in Table 15 under Population 6
Summary
Many research papers have appeared in the literature where authors have used the conventional and the nonconventional measures of the auxiliary variable to enhance the efficiency of estimators. Gupta and Shabbir [3] introduced a class of ratio-in-difference-type estimators using the conventional measures for the population mean. Singh et al [4] presented an improved family of exponential-ratio-type estimator in simple random sampling for population mean. Yadav and Kadilar [6] proposed an exponential family of ratio-type estimators by using conventional measures for estimating the population mean. Grover and Kaur [8] suggested a generalized class of exponential-ratio-type exponential estimators using the conventional measures for mean estimation. Irfan et al [10] suggested a generalized ratio-exponential-type estimator using the conventional measures. We propose a new generalized class of exponential-ratio-type estimators by using the conventional and the nonconventional measures of the auxiliary variable and compare our proposed estimator with several existing estimators.
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