Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study
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 estimatio...
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doaj-06ffa93658f44342908213cd7b5dd3212021-04-22T12:35:09ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2014-12-0144110.17713/ajs.v44i1.1528Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the StudyJehad Al-Jararha0Ala' Bataineh1Yarmouk UniversityDepartment of Statistics Yarmouk University, Irbid, Jordan 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. http://www.ajs.or.at/index.php/ajs/article/view/15 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Jehad Al-Jararha Ala' Bataineh |
spellingShingle |
Jehad Al-Jararha Ala' Bataineh Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study Austrian Journal of Statistics |
author_facet |
Jehad Al-Jararha Ala' Bataineh |
author_sort |
Jehad Al-Jararha |
title |
Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study |
title_short |
Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study |
title_full |
Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study |
title_fullStr |
Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study |
title_full_unstemmed |
Estimation of Finite Population Ratio When Other Auxiliary Variables are Available in the Study |
title_sort |
estimation of finite population ratio when other auxiliary variables are available in the study |
publisher |
Austrian Statistical Society |
series |
Austrian Journal of Statistics |
issn |
1026-597X |
publishDate |
2014-12-01 |
description |
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.
|
url |
http://www.ajs.or.at/index.php/ajs/article/view/15 |
work_keys_str_mv |
AT jehadaljararha estimationoffinitepopulationratiowhenotherauxiliaryvariablesareavailableinthestudy AT alabataineh estimationoffinitepopulationratiowhenotherauxiliaryvariablesareavailableinthestudy |
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1721514306793635840 |