Journal of Applied Probability

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

Marcus C. Christiansen and Nicola Loperfido

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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

Permanent link to this document
https://projecteuclid.org/euclid.jap/1402578637

Digital Object Identifier
doi:10.1239/jap/1402578637

Mathematical Reviews number (MathSciNet)
MR3217779

Zentralblatt MATH identifier
1304.60030

Subjects
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)

Keywords
Central limit theorem Cramer's condition order of convergence skew normal skewness third-order tensor

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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