TITLE:
Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling
AUTHORS:
Tonui Kiplangat Milton, Romanus Otieno Odhiambo, George Otieno Orwa
KEYWORDS:
Modified Ratio Type Variance Estimator, Study Variable, Auxiliary Variable, Kurtosis, Median, Bias, Mean Squared Error (MSE), Percentage Relative Efficiency (PRE), Simple Random Sampling
JOURNAL NAME:
Open Journal of Statistics,
Vol.7 No.6,
December
4,
2017
ABSTRACT: In this study we have proposed a modified ratio type estimator for
population variance of the study variable y under simple random sampling without replacement making use of coefficient of
kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order
of Taylor’s series expansion. The efficiency conditions derived theoretically under
which the proposed estimator performs better than existing estimators.
Empirical studies have been done using real populations to demonstrate the
performance of the developed estimator in comparison with the existing estimators.
The proposed estimator as illustrated by the empirical studies performs better
than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared
Error and the highest Percentage Relative Efficiency. The developed estimator
therefore is suitable to be applied to situations in which the variable of
interest has a positive correlation with the auxiliary variable.