On the density of the sum of two independent Student t-random vectors
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In this paper, we find an expression for the density of the sum of two independent d-dimensional
Student t-random vectors X and Y with arbitrary degrees of freedom. As a
byproduct we also obtain an expression for the density of the sum N+X, where N is normal
and X is an independent Student t-vector. In both cases the density is given as an infinite
series $\sum_{n=0}^\infty c_nf_n$
where f_n is a sequence of probability densities on R^d and c_n 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.
Original language | English |
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Journal | Statistics & Probability Letters |
Volume | 80 |
Pages (from-to) | 1043-1055 |
ISSN | 0167-7152 |
DOIs | |
Publication status | Published - 2010 |
- Faculty of Science - Student t-distribution, convolution, infinite divisibility
Research areas
ID: 22613413