On the density of the sum of two independent Student t-random vectors

C. Berg and C. Vignat

Statistics & Probability Letters, 2010, vol. 80, issue 13-14, 1043-1055

Abstract: In this paper, we find an expression for the density of the sum of two independent d-dimensional Student t-random vectors and with arbitrary degrees of freedom. As a byproduct we also obtain an expression for the density of the sum , where is normal and is an independent Student t-vector. In both cases the density is given as an infinite series where fn is a sequence of probability densities on and (cn) is a sequence of positive numbers of sum 1, i.e. the distribution of a non-negative integer-valued random variable C, which turns out to be infinitely divisible for d=1 and d=2. When d=1 and the degrees of freedom of the Student variables are equal, we recover an old result of Ruben.

Keywords: Student; t-distributions; Convolution; Infinite; divisibility (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (3)

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