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

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ID: 70450
2019
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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 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.
Reference Key
bonetti2019computingroyal Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Bonetti, Marco;Cirillo, Pasquale;Ogay, Anton;
Journal Royal Society open science
Year 2019
DOI
10.1098/rsos.190198
URL
Keywords
exact probability multinomial counts urns

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