Improved Exponential Type Estimators for Estimation of Population Mean with and without Use of Auxiliary Information

Abstract

newline The present study is an attempt to proposesome improvedexponential type estimators for estimating the population mean precisely under the condition with and without the use of auxiliary information. The large sample properties viz. Biasand MSE forthe proposed estimators have beenobtained and compared with the estimators existing in literature both theoretically as well as empirically using different populations accordingly. newline newlineIt is well known that the auxiliaryinformation may be quantitative or qualitative in nature. When the auxiliary information is quantitative, the exponential ratio and product type estimators tir(i=1, 2) and tip respectively have been proposed.For qualitative, the proportion based exponential ratio and product type estimators TirandTiprespectively are proposed. If the population proportion (P) of the auxiliary variable is not knownthen the double samplingexponential ratio and product type estimatorsTir(d) and Tip(d)respectively have been proposed. newline newlineThe dual unbiased exponential type estimators tdeiand Tdei are proposed in case the auxiliary variable is quantitative and qualitative in nature respectively. If P is not known, the proportion based double samplingexponential type estimators Tdei(d)have been proposed. newline newline In the absence of auxiliary variable, theexponential type estimatorstpriand the unbiased exponential type estimators tuei have been proposed. newline newlineThe proposed estimators are found efficient both theoretically and empirically than the conventional exponential estimators of BahlandTuteja (1991), Watson (1937), Cochran (1940), Robson (1957), Reddy (1974), Naik and Gupta (1996)Singh et al. (2007), Singh et al. (2009), Onyeka (2013), Subramani (2016) and ZamanandKadilar (2019) accordingly. newline