Variance Estimator Using Tri-mean and Inter Quartile Range of Auxiliary Variable

Abstract

Background: Whenever the population is large and it is very time taking and costly to take observation on each unit of the population then sampling is the only way to get the appropriate estimate of the population parameter under consideration. Many authors have given many estimators for estimating population variance with greater efficiency.

Objective: The objective of the study is to search for more efficient estimator than the competing estimators of population variance of study variable.

Materials and Methods: The estimator utilizing information on tri-mean and inter quartile range of auxiliary variable has been is developed. The expressions for the bias and mean squared error (MSE) of the proposed estimator have been derived up to the first order of approximation. A theoretical comparison of the proposed estimator has been made with the competing estimators of population variance.

Results: The theoretical findings have been justified with the help of numerical example from some natural populations. It has been found that the proposed estimator is best among the competing estimators of population variance as it has least mean squared error among them.

Conclusion: Since the proposed estimator is best among the competing estimator of the population variance, therefore it must be used for the improved estimation of population variance.

Nepalese Journal of Statistics, 2017, Vol. 1, 83-91