## Some results on the truncated multivariate $$t$$ distribution.(English)Zbl 1229.62068

Summary: The use of truncated distributions arises often in a wide variety of scientific problems. In the literature, there are a lot of sampling schemes and proposals developed for various specific truncated distributions. So far, however, the study of the truncated multivariate $$t$$ (TMVT) distribution is rarely discussed. We first present general formulae for computing the first two moments of the TMVT distribution under the double truncation. We formulate the results as analytic matrix expressions, which can be directly computed in existing software. Results for the left and right truncation can be viewed as special cases. We then apply the slice sampling algorithm to generate random variates from the TMVT distribution by introducing auxiliary variables. This strategic approach can result in a series of full conditional densities that are of uniform distributions. Finally, several examples and practical applications are given to illustrate the effectiveness and importance of the proposed results.

### MSC:

 62H10 Multivariate distribution of statistics 62F15 Bayesian inference 65C60 Computational problems in statistics (MSC2010)
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### References:

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