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Infinite divisibility of skew Gaussian and Laplace laws

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  • Kozubowski, Tomasz J.
  • Nolan, John P.

Abstract

We study infinite divisibility of skew distributions given by the density function g[lambda](x)=2f(x)F([lambda]x), , where f and F are the density and distribution functions of (symmetric) normal or Laplace laws. It turns out that although the symmetric laws are both infinitely divisible (ID), the skew normal is not ID but the skew Laplace is ID. A new stochastic representation for skewed Laplace distributions is given, which is independently useful for simulation. We also show that the skew Laplace laws are self-decomposable only for [lambda] below a specified threshold.

Suggested Citation

  • Kozubowski, Tomasz J. & Nolan, John P., 2008. "Infinite divisibility of skew Gaussian and Laplace laws," Statistics & Probability Letters, Elsevier, vol. 78(6), pages 654-660, April.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:6:p:654-660
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    2. V. Nekoukhou & M. Alamatsaz, 2012. "A family of skew-symmetric-Laplace distributions," Statistical Papers, Springer, vol. 53(3), pages 685-696, August.
    3. Hossein Negarestani & Ahad Jamalizadeh & Sobhan Shafiei & Narayanaswamy Balakrishnan, 2019. "Mean mixtures of normal distributions: properties, inference and application," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(4), pages 501-528, May.

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