The Distribution of Randomly Weighted Averages on Random Independent Vectors with Dirichlet Distributions

Subject Areas : International Journal of Industrial Mathematics

Hazhir Homei ¹ , هاوری حداد ² , M. H. Behzadi ³ , Rahman Farnoosh ⁴

1 - Department of Statistics, Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Ira
2 - دانشگاه آزاد اسلامی واحد علوم و تحقیقات، دانشکده علوم، تهران، ایران
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.

Received: 2022-01-19 Accepted : 2024-08-05 Published : 2024-09-21

Keywords: Randomly Weighted Averages, Basu&rsquo, s Theorem, Mathematical Induction, Dirichlet Distribution, Moments Method.,

Abstract :

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.