### Abstract

We propose optimal procedures to achieve the goal of partitioning k multivariate normal populations into two disjoint subsets with respect to a given standard vector. Definition of good or bad multivariate normal populations is given according to their Mahalanobis distances to a known standard vector as being small or large. Partitioning k multivariate normal populations is reduced to partitioning k non-central Chi-square or non-central F distributions with respect to the corresponding non-centrality parameters depending on whether the covariance matrices are known or unknown. The minimum required sample size for each population is determined to ensure that the probability of correct decision attains a certain level. An example is given to illustrate our procedures.

Original language | English (US) |
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Pages (from-to) | 2227-2234 |

Number of pages | 8 |

Journal | Journal of Statistical Planning and Inference |

Volume | 139 |

Issue number | 7 |

DOIs | |

State | Published - Jul 1 2009 |

### Keywords

- Correct decision
- Optimal procedure
- Sample size determination
- Stochastically increasing

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty
- Applied Mathematics