On the density of the sum of two independent Student t-random vectors
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On the density of the sum of two independent Student t-random vectors. / Berg, Christian; Vignat, Christophe.
In: Statistics & Probability Letters, Vol. 80, 2010, p. 1043-1055.Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - On the density of the sum of two independent Student t-random vectors
AU - Berg, Christian
AU - Vignat, Christophe
PY - 2010
Y1 - 2010
N2 - In this paper, we find an expression for the density of the sum of two independent d-dimensionalStudent t-random vectors X and Y with arbitrary degrees of freedom. As abyproduct we also obtain an expression for the density of the sum N+X, where N is normaland X is an independent Student t-vector. In both cases the density is given as an infiniteseries $\sum_{n=0}^\infty c_nf_n$where f_n is a sequence of probability densities on R^d and c_n is a sequence of positivenumbers of sum 1, i.e. the distribution of a non-negative integer-valued random variableC, which turns out to be infinitely divisible for d=1 and d=2. When d=1 and thedegrees of freedom of the Student variables are equal, we recover an old result of Ruben.
AB - In this paper, we find an expression for the density of the sum of two independent d-dimensionalStudent t-random vectors X and Y with arbitrary degrees of freedom. As abyproduct we also obtain an expression for the density of the sum N+X, where N is normaland X is an independent Student t-vector. In both cases the density is given as an infiniteseries $\sum_{n=0}^\infty c_nf_n$where f_n is a sequence of probability densities on R^d and c_n is a sequence of positivenumbers of sum 1, i.e. the distribution of a non-negative integer-valued random variableC, which turns out to be infinitely divisible for d=1 and d=2. When d=1 and thedegrees of freedom of the Student variables are equal, we recover an old result of Ruben.
KW - Faculty of Science
KW - sandsynlighedsregning, Student t-fordelinger
KW - Student t-distribution, convolution, infinite divisibility
U2 - 10.1016/j.spl.2010.02.019
DO - 10.1016/j.spl.2010.02.019
M3 - Journal article
VL - 80
SP - 1043
EP - 1055
JO - Statistics & Probability Letters
JF - Statistics & Probability Letters
SN - 0167-7152
ER -
ID: 22613413