Computing the exact distributions of some functions of the ordered multinomial counts: Maximum, minimum, range and sums of order statistics

M. Bonetti, Pasquale Cirillo, Anton Ogay

Research output: Contribution to journalArticleScientificpeer-review

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Abstract

Starting from seminal neglected work by Rappeport (Rappeport 1968 Algorithms and computational procedures for the application of order statistics to queuing problems. PhD thesis, New York University), we revisit and expand on the exact algorithms to compute the distribution of the maximum, the minimum, the range and the sum of the J largest order statistics of a multinomial random vector under the hypothesis of equiprobability. Our exact results can be useful in all those situations in which the multinomial distribution plays an important role, from goodness-of-fit tests to the study of Poisson processes, with applications spanning from biostatistics to finance. We describe the algorithms, motivate their use in statistical testing and illustrate two applications. We also provide the codes and ready-to-use tables of critical values.
Original languageEnglish
Article number190198
Pages (from-to)1-32
Number of pages32
JournalRoyal Society Open Science
Volume6
Issue number10
DOIs
Publication statusPublished - 2019

Keywords

  • Exact probability
  • Multinomial counts
  • Urns

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