Estimation of Population Mean Using Information on Auxiliary Attribute

Abstract

We consider the problem of estimating the finite population mean when some information on auxiliary attribute is available. We obtain the mean square error (MSE) equation for the proposed estimators. It has been shown that the proposed estimator is better than Naik and Gupta (1996), Singh et al. (2008), Abd-Elfattah (2010) estimators. The results have been illustrated numerically by taking some empirical population considered in the literature.

Generalized exponential estimators for the finite population mean

“…All of the suggested estimators have the same minimum MSE equation. Considering MSE equations, the suggested exponential estimators are always more efficient than those of the sample mean, the ratio and product estimators of Naik and Gupta (1996), the ratio and product estimators of Singh et al (2007) and the ratio exponential estimators of Zaman and Kadilar (2019a), under all the conditions. The results presented here support these conclusions by theoretical development and numerical analysis.…”

“…the number of teachers 1 , if the number of teachers is more than 60 0 , otherwise. From the Table 4, it is observed that the suggested exponential estimators , 1,2, … ,10 perform better than the usual unbiased estimator , ratio and product estimators of Naik and Gupta (1996), ratio and product estimators suggested by Singh et al (2007) and the ratio exponential estimators presented in Zaman and Kadilar (2019a). Finally, it is inferred that the suggested estimators perform better than the considered ratio estimators in all conditions, because the conditions given in Section 3 are always satisfied.…”

“…Considering Bahl and Tuteja (1991), Singh et al (2007) suggested the following ratio estimator when the study variable and the auxiliary attribute are positively correlated.…”

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This study proposes a new class of exponential-type estimators in simple random sampling for the estimation of the population mean of the study variable using information of the population proportion possessing certain attributes. Theoretically, mean squared error (MSE) equations of the suggested ratio exponential estimators are obtained and compared with the Naik and Gupta (1996) ratio and product estimators, the ratio and product exponential estimator presented in Singh et al (2007) and the ratio exponential estimators presented in Zaman and Kadilar (2019a). As a result of these comparisons, it is observed that the proposed estimators always produce more efficient results than the others.

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Estimating Population Coefficient of Variation Using a Single Auxiliary Variable in Simple Random Sampling

“…It is a prominent fact in the theory of sample surveys that suitable use of auxiliary information increases the efficiency of the estimators used for estimating the unknown population parameters. Some important works illustrating use of auxiliary information at estimation stage are , Singh et al (2007), Khoshnevisan et al (2007), Singh et al (2009), Singh and Kumar (2011), Malik and Singh (2013) and Singh et al (2018). Over a vast period of time a substantial amount of work has been done by several authors for the estimation of population mean, population variance but little attention has been given to the estimation of the population coefficient of variation.…”