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

TY - JOUR

T1 - On the density of the sum of two independent Student t-random vectors

AU - Berg, Christian

AU - Vignat, Christophe

PY - 2010/7

Y1 - 2010/7

N2 - 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, where fn is a sequence of probability densities on Rd 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.

AB - 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, where fn is a sequence of probability densities on Rd 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.

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

SN - 0167-7152

VL - 80

SP - 1043

EP - 1055

JO - Statistics & Probability Letters

JF - Statistics & Probability Letters

ER -