Journal of the Korean Statistical Society

The Korean Statistical Society (한국통계학회)
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GENERAL FAMILIES OF CHAIN RATIO TYPE ESTIMATORS OF THE POPULATION MEAN WITH KNOWN COEFFICIENT OF VARIATION OF THE SECOND AUXILIARY VARIABLE IN TWO PHASE SAMPLING

  • Singh Housila P. (School of Studies in Statistics, Vikram University) ;
  • Singh Sarjinder (Department of Statistics and Computer Networking, St. Cloud State University) ;
  • Kim, Jong-Min (Division of Science and Mathematics University of Minnesota)
  • Published : 2006.12.31
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Abstract

In this paper we have suggested a family of chain estimators of the population mean $\bar{Y}$ of a study variate y using two auxiliary variates in two phase (double) sampling assuming that the coefficient of variation of the second auxiliary variable is known. It is well known that chain estimators are traditionally formulated when the population mean $\bar{X}_1$ of one of the two auxiliary variables, say $x_1$, is not known but the population mean $\bar{X}_2$ of the other auxiliary variate $x_2$ is available and $x_1$ has higher degree of positive correlation with the study variate y than $x_2$ has with y, $x_2$ being closely related to $x_1$. Here the classes are constructed when the population mean $\bar{X}_1\;of\;X_1$ is not known and the coefficient of variation $C_{x2}\;of\;X_2$ is known instead of population mean $\bar{X}_2$. Asymptotic expressions for the bias and mean square error (MSE) of the suggested family have been obtained. An asymptotic optimum estimator (AOE) is also identified with its MSE formula. The optimum sample sizes of the preliminary and final samples have been derived under a linear cost function. An empirical study has been carried out to show the superiority of the constructed estimator over others.

Keywords

References

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