Characterization of the Three-Variate Inverted Dirichlet Distributions
DOI:
https://doi.org/10.52737/18291163-2023.15.12-1-9Keywords:
Characterization of Probability Distributions, Functional Equation, Independence, Inverted Dirichlet Distribution, TransformationAbstract
In this paper, we prove a characterization of three-variate inverted Dirichlet distributions by an independence property. The main technical challenge was a problem involving the solution of a related functional equation.
References
T. Bdiri and N. Bouguila, Positive vectors clustering using inverted Dirichlet finite mixture models. Expert Systems with Applications, 39 (2012), no. 2, pp. 1869-1882. https://doi.org/10.1016/j.eswa.2011.08.063
M. Ben Farah, Non-central Dirichlet type 2 distributions on symmetric matrices. J. Math. Anal. Appl., 396 (2012), no. 1, pp. 84-92. https://doi.org/10.1016/j.jmaa.2012.05.069
M. Ben Farah and A. Hassairi, On the Dirichlet distributions on symmetric matrices. J. Statist. Plann. Inf., 139 (2009), no. 8, pp. 2559-2570. https://doi.org/10.1016/j.jspi.2008.11.014
J.N. Darroch and D. Ratcliff, A characterization of the Dirichlet distribution. J. Am. Stat. Assoc., 66 (1971), pp. 641-643.
B. Kolodziejek, Characterization of beta distribution on symmetric cones. J. Multivar. Anal., 143 (2016), pp. 414-423.
G. Letac and J. Wesolowski, An independence property for the product of GIG and gamma laws. Ann. Prob., 28 (2000), no. 3, pp. 1371-1383. https://doi.org/10.1214/aop/1019160339
E. Lukacs, A characterization of the gamma distribution. Ann. Math Statist., 26 (1955), no. 2, pp. 319-324. https://doi.org/10.1214/aoms/1177728549
I. Olkin and H. Rubin, A characterization of the Wishart distribution. Ann. Math. Statist., 33 (1962), no. 4, pp. 1272-1280. https://doi.org/10.1214/aoms/1177704359
G.G. Tiao and I. Guttman, The inverted Dirichlet distribution with applications. J. Am. Stat. Assoc., 60 (1965), pp. 793-805. With corrigendum, pp. 1251-1252.
J. Wesolowski, On a functional equation related to an independence property for beta distributions. Aequat. Math., 66 (2003), pp. 156-163. https://doi.org/10.1007/s00010-003-2664-z
Downloads
Published
Issue
Section
License
Copyright (c) 2023 Armenian Journal of Mathematics
This work is licensed under a Creative Commons Attribution 4.0 International License.
How to Cite
