| Summary: | 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.
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