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On Some New Properties of the Beta Distribution by Włodzimierz Krysicki is a Mathematics article available to read on EtoBox.
What is On Some New Properties of the Beta Distribution about?
The ÿrst aim of this paper is to show how to present a random variable with the beta distribution (of the ÿrst kind) as a ÿnite or inÿnite product of independent random variable's (r.v.)'s X k , where k ∈ [1; 2; : : : ; n] or k ∈ N. Such a presentation of an r.v. with the gamma distribution in the form of an inÿnite product of r.v.'s was used by Lu and Richards [Lu, I-Li, Richards, D., 1993. Random discriminants. Ann. Statist. 21 (4) 1992-2000] to deÿne the square of the Vandermonde determinant with random elements. Next, the convergence of the series ∞ 1 (1=2 k )ln X k to ln X with probability one has been proved. Finally, the Mieshalkin-Rogozin theorem [Mieshalkin, D., Rogozin, B.A., 1963. Ocenka razstajania mie żdu funkcjami raspredelenia po blizosti ich charakteristiczeskich funkcji i jeje primenenie k centralnoj predielnoj teoremie. (in Predelnyje teoremy verojatnostej. Taszkent. Akad Nauk Uzbec. SSR)], modiÿed in this paper, has been applied to the beta distribution.
Who reads On Some New Properties of the Beta Distribution?
It is typically read by researchers, students, and practitioners in Mathematics.
- Author
- Włodzimierz Krysicki
- Publisher
- Elsevier Science; Elsevier ; Elsevier BV (ISSN 0167-7152)
- Published
- 1999
- Language
- EN
- Field
- Mathematics (Physical Sciences)