Abstract
In the studies in literature up to date arithmetic population mean of auxiliary variable is used to obtain the proportional estimators. In this paper geometric mean, harmonic mean and quadratic mean is used as well as arithmetic population mean. Using geometric mean, harmonic mean and quadratic mean do not affect the variance of ratio estimator ( ). However new approaches are obtained for the estimation and variance of the dependent variable when these means are used as well as arithmetic population mean. In the application, the mean number of teaching staff of the departments in Ondokuz Mayis University is estimated by auxiliary variable which is the number of students in the departments. In addition the variances of proportional estimation method are obtained and interpreted by using population arithmetic mean, geometric mean, harmonic and quadratic mean.
Highlights
One of the basic estimation method, using auxiliary variable to estimate the population mean, in simple random sampling is the proportional estimator method
In this paper geometric mean, harmonic mean and quadratic mean are used as the population mean as well as arithmetic mean
“Kadılar and Çıngı (2005) developed a new estimator, for population mean in two variable regression estimator, using the two auxiliary variable multiplicative estimator proposed by Dayveh et al [6]”
Summary
One of the basic estimation method, using auxiliary variable to estimate the population mean, in simple random sampling is the proportional estimator method. In all studies regarding the proportional estimators, arithmetic mean is chosen as the population mean of the auxiliary variable. In this paper geometric mean, harmonic mean and quadratic mean are used as the population mean as well as arithmetic mean Using these means as well as arithmetic will not change the variance of proportional estimator. ), new approaches are obtained for the estimation of the dependent variable and its variance. “Kadılar and Çıngı (2005) developed a new estimator, for population mean in two variable regression estimator, using the two auxiliary variable multiplicative estimator proposed by Dayveh et al [6]”. “Beale (1962) and Tin (1965) used variation coefficients of dependent variable and independent variable as auxiliary variable to propose new proportional estimators for population mean [13, 14]”.
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