Author(s)

Tonui Kiplangat Milton^1*, Romanus Otieno Odhiambo², George Otieno Orwa²

¹Pan African University, Institute for Basic Sciences, Technology and Innovation (PAUISTI), Nairobi, Kenya.
²Department of Statistics and Actuarial Science, Jomo Kenyatta University of Agriculture and Technology, Nairobi, Kenya.

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.

Modified Ratio Type Variance Estimator, Study Variable, Auxiliary Variable, Kurtosis, Median, Bias, Mean Squared Error (MSE), Percentage Relative Efficiency (PRE), Simple Random Sampling

Milton, T. , Odhiambo, R. and Orwa, G. (2017) Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling. Open Journal of Statistics, 7, 944-955. doi: 10.4236/ojs.2017.76066.