Journal of Applied Probability
- J. Appl. Probab.
- Volume 51, Number 2 (2014), 466-482.
Improved approximation of the sum of random vectors by the skew normal distribution
We study the properties of the multivariate skew normal distribution as an approximation to the distribution of the sum of n independent, identically distributed random vectors. More precisely, we establish conditions ensuring that the uniform distance between the two distribution functions converges to 0 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.
J. Appl. Probab., Volume 51, Number 2 (2014), 466-482.
First available in Project Euclid: 12 June 2014
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60F05: Central limit and other weak theorems 60B12: Limit theorems for vector-valued random variables (infinite- dimensional case)
Secondary: 15A69: Multilinear algebra, tensor products 62E17: Approximations to distributions (nonasymptotic)
Christiansen, Marcus C.; Loperfido, Nicola. Improved approximation of the sum of random vectors by the skew normal distribution. J. Appl. Probab. 51 (2014), no. 2, 466--482. doi:10.1239/jap/1402578637. https://projecteuclid.org/euclid.jap/1402578637