On the Conditional Distribution of the Multivariate $t$ Distribution

Peng Ding

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arXiv · 1604.00561

On the Conditional Distribution of the Multivariate $t$ Distribution

Peng Ding

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Abstract

As alternatives to the normal distributions, $t$ distributions are widely applied in robust analysis for data with outliers or heavy tails. The properties of the multivariate $t$ distribution are well documented in Kotz and Nadarajah's book, which, however, states a wrong conclusion about the conditional distribution of the multivariate $t$ distribution. Previous literature has recognized that the conditional distribution of the multivariate $t$ distribution also follows the multivariate $t$ distribution. We provide an intuitive proof without directly manipulating the complicated density function of the multivariate $t$ distribution.

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Peng Ding. 2016-04-02. On the Conditional Distribution of the Multivariate $t$ Distribution. https://arxiv.org/abs/1604.00561

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