The History of the Dirichlet and Liouville Distributions

Rameshwar D. Gupta and Donald St. P. Richards

International Statistical Review, 2001, vol. 69, issue 3, 433-446

Abstract: The Dirichlet distributions have long been the subject of intense scrutiny in statistics and probability. Despite the enormous interest in, and wide‐ranging applications of, these distributions, little appears to be known about their history. In this article we review the development of the Dirichlet distributions and their companions, the Liouville distributions. After reviewing some integral formulas of Dirichlet and Liouville, we survey the theory and applications of these distributions in statistics. Les distributions de Dirichlet font depuis longtemps l'objet d'études approfondies en statistique et en probabilité. En dépit de l'énorme intéêt portéà ces distributions et de leurs applications variées, on sait peu de choses de leur histoire. Dans se article, on examine le développement des distributions de Dirichlet, ainsi que des distributions associées de liouville. Aprés avoir rappelé quelques formules d'intégrales de Dirichlet et Lioville, on brosse un panorama de la théorie et des applications de ces distributions en statistique.

Date: 2001
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