### Abstract

An inverse sampling procedure R is proposed for selecting a randomsize subset which contains the least probable cell (i.e., the cell with the smallest cell probabilities) from a multinomial distribution with k cells. Type 2-Dirichlet integrals are used (i) to express the probability of a correct selection in terms of integrals with parameters only in the limits of integration, (ii) to prove that the least favorable configuration under R is the so-called slippage configuration with k equal cell probabilities, and (iii) to express exactly the expectation of the total number of observations required and the expectation of the subset size under the procedure R.

Original language | English (US) |
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Pages (from-to) | 303-314 |

Number of pages | 12 |

Journal | Annals of the Institute of Statistical Mathematics |

Volume | 37 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1985 |

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### Keywords

- Dirichlet integral
- inverse sampling
- least favorable configuration
- multinomial distribution
- subset selection formulation

### ASJC Scopus subject areas

- Statistics and Probability
- Mathematics(all)