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Title:	A revisit of the distribution of linear combinations of Dirichlet components
Authors:	姜志銘 Jiang, Thomas J. Kuo, Kun-Lin
Contributors:	應數系
Keywords:	c-characteristic function;Dirichlet distribution;inversion formula
Date:	2017
Issue Date:	2017-07-12 15:13:34 (UTC+8)
Abstract:	Provost and Cheong show the importance of the distribution of linear combinations of components of a Dirichlet random vector to quadratic forms and their ratios in statistics, which can be applied in a variety of contexts. The c-characteristic function has been shown to be very useful and more practical in some distributions that are hard to manage with the traditional characteristic functions. In particular, the distribution of linear combinations of components of a Dirichlet random vector has a very simple c-characteristic function expression. We first provide its inversion formula which is practical in determining the distribution function of a random variable when its c-characteristic function is known. We then use this inversion formula to find an expression of probability density function of linear combinations of components of any Dirichlet vector. This would generalize the results given by Provost and Cheong.
Relation:	Communications in Statistics - Theory and Methods, Volume 47, Issue 3, Pages 509-520
Data Type:	article
DOI 連結:	http://dx.doi.org/10.1080/03610926.2017.1307402
DOI:	10.1080/03610926.2017.1307402
Appears in Collections:	[應用數學系] 期刊論文

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