Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study

• Main Authors: Jehad Al-Jararha, Ala' Bataineh
• Format: Article
• Language: English
• Published: Austrian Statistical Society 2014-12-01
• Series: Austrian Journal of Statistics
• Online Access: http://www.ajs.or.at/index.php/ajs/article/view/15

The estimation of the population total $t_y,$ by using one or more auxiliary variables, and the population ratio $\theta_{xy}=t_y/t_x,$ $t_x$ is the population total for the auxiliary variable $X$, for a finite population are heavily discussed in the literature. In this paper, the idea of estimation the finite population ratio $\theta_{xy}$ is extended to use the availability of auxiliary variable $Z$ in the study, such auxiliary variable  is not used in the  definition of the population ratio. This idea may be  supported by the fact that  the variable $Z$  is highly correlated with the interest  variable $Y$ than the correlation between the variables $X$ and  $Y.$  The availability of such auxiliary variable can be used to improve the precision of the  estimation of the population ratio.  To our knowledge, this idea is  not discussed in the literature.   The bias, variance and the mean squares error  are given for our  approach. Simulation from real data set,  the empirical relative bias and  the empirical relative mean squares  error are computed for our approach and different estimators proposed in the literature  for estimating the population  ratio $\theta_{xy}.$ Analytically and the simulation results show that, by  suitable choices, our approach gives negligible bias and has less  mean squares error.