Logarithmic Ratio-Type Estimator of Population Coefficient of Variation
M. A. Yunusa
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.
A. Audu *
Department of Mathematics, Usmanu Danfodiyo University, Sokoto, Nigeria.
N. Musa
School of Health Management, College of Health Sc. and Tech., Tsafe, Nigeria.
D. O. Beki
Department of Statistics, Kwara State Polytechnic Ilorin, Nigeria.
A. Rashida
State College of Basic and Remedial Studies, Sokoto, Nigeria.
A. B. Bello
State College of Basic and Remedial Studies, Sokoto, Nigeria.
M. U. Hairullahi
State College of Basic and Remedial Studies, Sokoto, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
The estimation of population coefficient of variation is one of the challenging aspects in sampling survey techniques for the past decades and much effort has been employed to develop estimators to produce its efficient estimate. In this paper, we proposed logarithmic ratio type estimator for the estimating population coefficient of variation using logarithm transformation on the both population and sample variances of the auxiliary character. The expression for the mean squared error (MSE) of the proposed estimator has been derived using Taylor series first order approximation approach. Efficiency conditions of the proposed estimator over other estimators in the study has also been derived. The empirical study was conducted using two-sets of populations and the results showed that the proposed estimator is more efficient. This result implies that, the estimate of proposed estimator will be closer to the true parameter than the estimates of other estimators in the study.
Keywords: Auxiliary variable, MSE, coefficient of variation; study variable, simple random sampling