Ratio Type Exponential Estimator for the Estimation of Finite Population Variance under Two-stage Sampling

Muhammad Jabbar ； Javid Shabbir ； Zaheer Ahmed ； Zainab Rehman

《Research Journal of Applied Sciences, Engineering and Technology》 7卷19期 (2014/05) Pp. 4095-4099

並列摘要

In this study we propose an improved exponential ratio type estimator in estimating the finite population variance in two stage sampling under two cases: (i) when sum of the weights cannot equal to one and (ii) when sum of the weights are equal to one. The bias and Mean Squared Error (MSE) are derived up to first order of approximation. The efficiency conditions, under which proposed estimator is more efficient than the usual sample variance estimator and regression estimator are obtained. Numerical and simulated studies are conducted to support the superiority of the estimators. Real data set is used to observe the performances of estimator.

並列關鍵字

Bias ； efficiency ； exponential ratio type estimator ； MSE ； two-stage sampling