AVERAGES FOR MULTIVARIATE RANDOM VECTORS WITH RANDOM WEIGHTS: DISTRIBUTIONAL CHARACTERIZATION AND APPLICATION

* We consider a random weights average of n independent continuous random vectors [X.sub.1], ..., [X.sub.n], where random weights are cuts of [0, 1] by an increasing sequence of the order statistics of a random sample from a uniform [0,1]. We employ the multivariate Stieltjes transform and Watson [1...

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Published inRevstat Vol. 18; no. 4; p. 453
Main Authors Soltani, A.R, Roozegar, Rasool
Format Journal Article
LanguageEnglish
Published Instituto Nacional de Estatistica 01.10.2020
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Abstract * We consider a random weights average of n independent continuous random vectors [X.sub.1], ..., [X.sub.n], where random weights are cuts of [0, 1] by an increasing sequence of the order statistics of a random sample from a uniform [0,1]. We employ the multivariate Stieltjes transform and Watson [15] celebrated formula involving the multivariate B-spline functions for distributional identification of multivariate random weights averages. We show that certain classes of Dirichlet and random scale stable random vectors are random weightes averages. Keywords: * multivariate weighted average with random weights; multivariate Cauchy Stieltjes transform; Dirichlet distribution; multivariate stable distributions. AMS Subject Classification: * 62H05, 46F12, 65R10.
AbstractList * We consider a random weights average of n independent continuous random vectors [X.sub.1], ..., [X.sub.n], where random weights are cuts of [0, 1] by an increasing sequence of the order statistics of a random sample from a uniform [0,1]. We employ the multivariate Stieltjes transform and Watson [15] celebrated formula involving the multivariate B-spline functions for distributional identification of multivariate random weights averages. We show that certain classes of Dirichlet and random scale stable random vectors are random weightes averages. Keywords: * multivariate weighted average with random weights; multivariate Cauchy Stieltjes transform; Dirichlet distribution; multivariate stable distributions. AMS Subject Classification: * 62H05, 46F12, 65R10.
* We consider a random weights average of n independent continuous random vectors [X.sub.1], ..., [X.sub.n], where random weights are cuts of [0, 1] by an increasing sequence of the order statistics of a random sample from a uniform [0,1]. We employ the multivariate Stieltjes transform and Watson [15] celebrated formula involving the multivariate B-spline functions for distributional identification of multivariate random weights averages. We show that certain classes of Dirichlet and random scale stable random vectors are random weightes averages.
Audience Academic
Author Soltani, A.R
Roozegar, Rasool
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