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May 2021 On multivariate selection scale-mixtures of normal distributions
Roohollah Roozegar, Narayanaswamy Balakrishnan, Andriette Bekker, Ahad Jamalizadeh
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Braz. J. Probab. Stat. 35(2): 351-374 (May 2021). DOI: 10.1214/20-BJPS478


In this paper, we establish some results for multivariate selection scale-mixtures of normal distributions with arbitrary mixing variable. First, we discuss their stochastic representation in terms of multivariate selection normal distributions. Next, the conditional distributions as well as the first two moments of multivariate selection scale-mixtures of normal distributions are obtained when the selection set is an arbitrary rectangle in the q-dimensional Euclidean space of Rq. The unified skew-scale mixture of normal (SUSMN) distributions are subsequently discussed as a special case. As a subclass of SUSMN distributions, the class of unified skew-symmetric generalized hyperbolic (SUSGH) distributions are studied in detail. Finally, we show that our results can be used to obtain moments of L-statistics and of multivariate concomitants from multivariate scale-mixtures of normal distributions.


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Roohollah Roozegar. Narayanaswamy Balakrishnan. Andriette Bekker. Ahad Jamalizadeh. "On multivariate selection scale-mixtures of normal distributions." Braz. J. Probab. Stat. 35 (2) 351 - 374, May 2021.


Received: 1 August 2019; Accepted: 1 June 2020; Published: May 2021
First available in Project Euclid: 24 March 2021

Digital Object Identifier: 10.1214/20-BJPS478

Keywords: concomitants of order statistics , inducedorder statistics , L-statistics , multivariate scale-mixtures of normal distributions , selection distribution , unified skew-scale mixtures of normal distributions

Rights: Copyright © 2021 Brazilian Statistical Association


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Vol.35 • No. 2 • May 2021
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