Aarhus University Seal / Aarhus Universitets segl

Improved approximation of the sum of random vectors by the skew-normal distribution

Marcus C. Christiansen
(University of Ulm)
Mandag, 10 september, 2012, at 14:00-15:00, in Aud. G1 (1532-116)
We study the properties of the multivariate skew-normal distribution as an approximation to the distribution of the sum of $n$ i.i.d. random vectors. More precisely, we establish conditions ensuring that the uniform distance between the two distribution functions converges to zero at a rate of $n^{-2/3}$. The advantage over the corresponding normal approximation is particularly relevant when the summands are skewed and $n$ is small, as illustrated for the special case of exponentially distributed random variables. Applications to some well-known multivariate distributions are also discussed.
Organiseret af: The T.N. Thiele Centre
Kontaktperson: Søren Asmussen