Efficient recursive computational algorithms for multivariate t and multivariate unified skew-t distributions with applications to inference

Mehdi Amiri (), Yaser Mehrali, Narayanaswamy Balakrishnan and Ahad Jamalizadeh
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Mehdi Amiri: University of Hormozgan
Yaser Mehrali: University of Khansar
Narayanaswamy Balakrishnan: McMaster University
Ahad Jamalizadeh: Shahid Bahonar University of Kerman

Computational Statistics, 2022, vol. 37, issue 1, No 7, 125-158

Abstract: Abstract In this paper, we establish efficient recursive algorithms for the computation of the cumulative distribution function (cdf) of multivariate Student’s t and multivariate unified skew-t distributions. The recurrence relations are over $$\nu $$ ν (the degrees of freedom), and starting from the explicit results for $$\nu $$ ν =1 and $$\nu $$ ν =2, they enable the recursive evaluation of the cdf for any positive integral value of $$\nu $$ ν . Using these, we obtain results for the computation of orthant probabilities of multivariate Student’s t distribution. We then demonstrate the usefulness of the established results in some problems involving order statistics and reliability systems. Finally, we use two real data sets to illustrate the methods established here.

Keywords: Hazard function; Multivariate Student’s t distribution; Multivariate unified skew-t distribution; Orthant probability; Order statistics; Recurrence relation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00180-021-01119-x

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