The estimation of the population total $t_y,$ by using one or moreauxiliary variables, and the population ratio $\theta_{xy}=t_y/t_x,$$t_x$ is the population total for the auxiliary variable $X$, for afinite population are heavily discussed in the literature. In thispaper, the idea of estimation the finite population ratio$\theta_{xy}$ is extended to use the availability of auxiliaryvariable $Z$ in the study, such auxiliary variable is not used inthe 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.
The univariate difference estimator of the population total under double sampling or inclusion probablilities when the total of the auxiliary variable is known