@article{Al-Jararha_Bataineh_2014, title={Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study}, volume={44}, url={https://www.ajs.or.at/index.php/ajs/article/view/vol44-1-4}, DOI={10.17713/ajs.v44i1.15}, abstractNote={<p>The estimation of the population total $t_y,$ by using one or more<br />auxiliary variables, and the population ratio $\theta_{xy}=t_y/t_x,$<br />$t_x$ is the population total for the auxiliary variable $X$, for a<br />finite population are heavily discussed in the literature. In this<br />paper, the idea of estimation the finite population ratio<br />$\theta_{xy}$ is extended to use the availability of auxiliary<br />variable $Z$ in the study, such auxiliary variable  is not used in<br />the<br /> definition of the population ratio. This idea may be  supported by the fact that<br /> the variable $Z$  is highly correlated with the interest<br /> variable $Y$ than the correlation between the variables $X$ and<br /> $Y.$<br /> The availability of such auxiliary variable can be used to improve the precision of the<br /> estimation of the population ratio.  To our knowledge, this idea is<br /> not discussed in the literature.</p><p><br />  The bias, variance and the mean squares error  are given for our<br /> approach. Simulation from real data set,  the empirical relative bias and  the empirical relative mean squares<br /> error are computed for our approach and different estimators proposed in the literature  for estimating the population<br /> ratio $\theta_{xy}.$ Analytically and the simulation results show that, by<br /> suitable choices, our approach gives negligible bias and has less<br /> mean squares error.</p><p> </p><p><br /> </p>}, number={1}, journal={Austrian Journal of Statistics}, author={Al-Jararha, Jehad and Bataineh, Ala’}, year={2014}, month={Dec.}, pages={33–46} }