Abstract
In this study an improved version of ratio type exponential estimator is been proposed for estimating average of study variable when the population parameter(s) information of second auxiliary variable is available. The proposed estimator compared with usual unbiased estimator and conventional ratio estimators numerically and hypothetically. The mean square error is also obtained and checked the efficiency of the proposed estimator with usual ratio, Singh and Vishwakarma (2007), Singh et al. (2008), Noor-ul-Amin and Hanif (2012), Yadav et al. (2013) and Sanaullah et al. (2015) estimators.
Highlights
The use of auxiliary variables often increases estimator’s efficiency when ratio and regression methods are considered for estimation in survey sampling
The product estimation method may be applied for negative linear relationship and the ratio method of estimation should be applied for the positive linear relationship between response and auxiliary variables
An improved exponential ratio type estimators using two auxiliary variables has been proposed by Sanaullah et al (2012) for estimating the populations mean in two phase sampling
Summary
The use of auxiliary variables often increases estimator’s efficiency when ratio and regression methods are considered for estimation in survey sampling. Estimation is done from large sample to observe the auxiliary variable x when the mean value X is unknown and later on a smaller sample is chosen from already drawn large sample for estimating y (study variate) This method is named as two phase or double sampling. The ratio estimators do not work efficiently under situations when the relationship is not linear between the auxiliary and study variables In such situations the exponential product and ratio estimators proposed by (Bahl & Tuteja, 1991). An improved exponential ratio type estimators using two auxiliary variables has been proposed by Sanaullah et al (2012) for estimating the populations mean in two phase sampling. A ratio type exponential estimator suggested by Bahl and Tuteja (1991) in two phase sampling is modified by Singh and Vishwakarma (2007) as: Ysv y2 exp é ê ë x1 x1. Efficiency of the proposed estimator has been checked mathematically with some existing estimators i.e. Y ,Ysv,Ys,YNHa ,YNHb ,YSA and YYad in section three, while empirical study and conclusion is discussed in section four and five respectively
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