On moments of folded and truncated multivariate Student-t distributions based on recurrence relations

The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that involve the density of multivariate Student-t distributions. The proposed techniques...

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Bibliographic Details
Published in:Metrika 2021-08, Vol.84 (6), p.825-850
Main Authors: Galarza, Christian E., Lin, Tsung-I, Wang, Wan-Lun, Lachos, Víctor H.
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics and Statistics
Multivariate analysis
Normal distribution
Probability Theory and Stochastic Processes
Statistics
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Summary:The use of the first two moments of the truncated multivariate Student-t distribution has attracted increasing attention from a wide range of applications. This paper develops recurrence relations for integrals that involve the density of multivariate Student-t distributions. The proposed techniques allow for fast computation of arbitrary-order product moments of folded and truncated multivariate Student-t distributions and offer explicit expressions of low-order moments of folded and truncated multivariate Student-t distributions. A real data example containing positive censored responses is applied to illustrate the effectiveness and importance of the proposed methods. An R MomTrunc package is developed and publicly available on the CRAN repository.
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-020-00802-1