Covariance matrix inequalities for functions of Beta random variables

2009 ◽  
Vol 79 (7) ◽  
pp. 873-879 ◽  
Author(s):  
Zhengyuan Wei ◽  
Xinsheng Zhang
Keyword(s):  
Covariance Matrix ◽  
Random Variables ◽  
Matrix Inequalities ◽  
Beta Random Variables

ANOVA models with random effects: an approach via symmetry

1986 ◽  
Vol 23 (A) ◽  
pp. 355-368 ◽  
Author(s):  
T. P. Speed
Keyword(s):  
Covariance Matrix ◽  
Random Effects ◽  
Spectral Decomposition ◽  
Linear Models ◽  
Random Variables ◽  
Components Of Variance

The standard ANOVA models with random effects for multi-indexed arrays of random variables with an arbitrary nesting structure on the indices are considered from the viewpoint of symmetry. It is found that the covariance matrix of such an array has sufficient symmetry to permit viewing the usual components of variance as a generalised spectrum and the linear models of random effects as a generalised spectral decomposition.

scholarly journals On the law of homogeneous stable functionals

2019 ◽  
Vol 23 ◽  
pp. 82-111
Author(s):  
Julien Letemplier ◽  
Thomas Simon
Keyword(s):  
Random Variables ◽  
Infinite Divisibility ◽  
Explicit Computation ◽  
Infinite Products ◽  
Stable Lévy Process ◽  
Distributional Properties ◽  
Lamperti Transformation ◽  
Beta Random Variables ◽  
Generalized Gamma Convolution ◽  
The Law

LetAbe theLq-functional of a stable Lévy process starting from one and killed when crossing zero. We observe thatAcan be represented as the independent quotient of two infinite products of renormalized Beta random variables. The proof relies on Markovian time change, the Lamperti transformation, and an explicit computation performed in [38] on perpetuities of hypergeometric Lévy processes. This representation allows us to retrieve several factorizations previously shown by various authors, and also to derive new ones. We emphasize the connections betweenAand more standard positive random variables. We also investigate the law of Riemannian integrals of stable subordinators. Finally, we derive several distributional properties ofArelated to infinite divisibility, self-decomposability, and the generalized Gamma convolution.

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