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On order relations between selection and inclusion probabilities in RHC sampling scheme. (English) Zbl 1046.62008
Summary: This is a sequel to T. J. Rao et al. [Metrika 38, 335–343 (1991; Zbl 0755.62020)] wherein various results connecting the inclusion probabilities \((\pi_i\) and \(\pi_{ij})\) and the selection probabilities \((p_i)\) in connection with the \(ppswor\) sampling scheme were discussed. We concentrate on the familiar Rao-Hartley-Cochran (RHC) sampling scheme for a general sample size \((n)\) and with random grouping. We establish, among other results, that \[ p_i> p_j \Leftrightarrow\pi_i>\pi_j,\qquad\text{for all }i\neq j;\tag{i} \] \[ p_i>p_j \Leftrightarrow\pi_{ik}>\pi_{jk},\quad\text{for all }k\neq i\neq j.\tag{ii} \]
MSC:
62D05 Sampling theory, sample surveys
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