Journal of Applied Probability

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

Abstract

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.

Article information

Source
J. Appl. Probab., Volume 51, Number 2 (2014), 466-482.

Dates
First available in Project Euclid: 12 June 2014

https://projecteuclid.org/euclid.jap/1402578637

Digital Object Identifier
doi:10.1239/jap/1402578637

Mathematical Reviews number (MathSciNet)
MR3217779

Zentralblatt MATH identifier
1304.60030

Citation

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

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