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June 2014 Improved approximation of the sum of random vectors by the skew normal distribution
Marcus C. Christiansen, Nicola Loperfido
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J. Appl. Probab. 51(2): 466-482 (June 2014). DOI: 10.1239/jap/1402578637

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.

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Marcus C. Christiansen. Nicola Loperfido. "Improved approximation of the sum of random vectors by the skew normal distribution." J. Appl. Probab. 51 (2) 466 - 482, June 2014. https://doi.org/10.1239/jap/1402578637

Information

Published: June 2014
First available in Project Euclid: 12 June 2014

zbMATH: 1304.60030
MathSciNet: MR3217779
Digital Object Identifier: 10.1239/jap/1402578637

Subjects:
Primary: 60B12, 60F05
Secondary: 15A69, 62E17

Rights: Copyright © 2014 Applied Probability Trust

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Vol.51 • No. 2 • June 2014
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