The Distribution of Randomly Weighted Averages on Random Independent Vectors with Dirichlet Distributions
محورهای موضوعی : مجله بین المللی ریاضیات صنعتی
Hazhir Homei
1
,
Hawre Hadad
2
,
M. H. Behzadi
3
,
Rahman Farnoosh
4
1 - Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz,
Ira
2 - Department of Statistics, Science and Research branch, Islamic Azad University, Tehran, Iran.
3 - Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran.
4 - School of Mathematics,
Iran University of Science and Technology, Tehran, Iran.
کلید واژه: Randomly Weighted Averages, Basu&rsquo, s Theorem, Mathematical Induction, Dirichlet Distribution, Moments Method.,
چکیده مقاله :
Randomly weighted averages of vectors with Dirichlet distributions will have the Dirichlet distribution when some certain conditions are satisfied. This has been recently proved by some statistical methods. In this paper, we present two simpler and shorter proofs for this fact, one by using Basu's theorem and one by mathematical induction.
Randomly weighted averages of vectors with Dirichlet distributions will have the Dirichlet distribution when some certain conditions are satisfied. This has been recently proved by some statistical methods. In this paper, we present two simpler and shorter proofs for this fact, one by using Basu's theorem and one by mathematical induction.
