Abstract
In this paper we suggest two modified estimators of the population mean using the power transformation based on ranked set sampling (RSS). The first order approximation of the bias and of the mean squared error of the proposed estimators are obtained. A generalized version of the suggested estimators by applying the power transformation is also presented. Theoretically, it is shown that these suggested estimators are more efficient than the estimators in simple random sampling (SRS). A numerical illustration is also carried out to demonstrate the merits of the proposed estimators using RSS over the usual estimators in SRS.
Highlights
The literature on ranked set sampling describes a great variety of techniques for using auxiliary information to obtain more efficient estimators
The classical ratio estimators given by Cochran (1940) for estimating the population mean Y is defined as yR = y x, where y is the sample mean for study variable y and x, X are the sample mean and population mean, respectively, for the auxiliary variable x
Singh and Kakran (1993) we suggest another new ratio estimator in ranked set sampling as yRSS,MM2 = y[n]
Summary
The literature on ranked set sampling describes a great variety of techniques for using auxiliary information to obtain more efficient estimators. Ranked set sampling was first suggested by McIntyre (1952) to increase the efficiency of estimator of population mean. We shall propose two modified estimators of population mean using power transformation using RSS based on auxiliary variable. When the population coefficient of variation Cx of the auxiliary variable x is known, Sisodia and Dwivedi (1981) give a modified ratio estimator for Y as P. Singh and Kakran (1993) developed a ratio-type estimator for Y as ySK = y. Utilizing the information on the coefficient of variation Cx and the coefficient of kurtosis β2(x) of the auxiliary variable x, Upadhyaya and Singh (1999) suggested the following ratio type estimators yU P 1. Where ρyx denotes the correlation coefficient between y and x
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