Exact and approximate distributions for the product of Dirichlet components

Saralees Nadarajah; Samuel Kotz

Kybernetika (2004)

  • Volume: 40, Issue: 6, page [735]-744
  • ISSN: 0023-5954

Abstract

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It is well known that X / ( X + Y ) has the beta distribution when X and Y follow the Dirichlet distribution. Linear combinations of the form α X + β Y have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product P = X Y (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose an approximation and show evidence to prove its robustness. This approximation will be useful especially to the practitioners of the Dirichlet distribution.

How to cite

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Nadarajah, Saralees, and Kotz, Samuel. "Exact and approximate distributions for the product of Dirichlet components." Kybernetika 40.6 (2004): [735]-744. <http://eudml.org/doc/33732>.

@article{Nadarajah2004,
abstract = {It is well known that $X/(X + Y)$ has the beta distribution when $X$ and $Y$ follow the Dirichlet distribution. Linear combinations of the form $\alpha X + \beta Y$ have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product $P = X Y$ (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose an approximation and show evidence to prove its robustness. This approximation will be useful especially to the practitioners of the Dirichlet distribution.},
author = {Nadarajah, Saralees, Kotz, Samuel},
journal = {Kybernetika},
keywords = {approximation; Dirichlet distribution; Gauss hypergeometric function; approximation; Dirichlet distribution; Gauss hypergeometric function},
language = {eng},
number = {6},
pages = {[735]-744},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Exact and approximate distributions for the product of Dirichlet components},
url = {http://eudml.org/doc/33732},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Nadarajah, Saralees
AU - Kotz, Samuel
TI - Exact and approximate distributions for the product of Dirichlet components
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 6
SP - [735]
EP - 744
AB - It is well known that $X/(X + Y)$ has the beta distribution when $X$ and $Y$ follow the Dirichlet distribution. Linear combinations of the form $\alpha X + \beta Y$ have also been studied in Provost and Cheong [S. B. Provost and Y.-H. Cheong: On the distribution of linear combinations of the components of a Dirichlet random vector. Canad. J. Statist. 28 (2000)]. In this paper, we derive the exact distribution of the product $P = X Y$ (involving the Gauss hypergeometric function) and the corresponding moment properties. We also propose an approximation and show evidence to prove its robustness. This approximation will be useful especially to the practitioners of the Dirichlet distribution.
LA - eng
KW - approximation; Dirichlet distribution; Gauss hypergeometric function; approximation; Dirichlet distribution; Gauss hypergeometric function
UR - http://eudml.org/doc/33732
ER -

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