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Estimation of the generalized Laplace distribution and its projection onto the circle

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  • Geraci, Marco

Abstract

The generalized Laplace (GL) distribution, which falls in the larger family of generalized hyperbolic distributions, provides a versatile model to deal with a variety of applications thanks to its shape parameters. The elliptically symmetric GL admits a polar representation that can be used to yield a circular distribution, which we call projected GL distribution. The latter does not appear to have been considered yet in practical applications. In this article, we explore an easy-to-implement maximum likelihood estimation strategy based on Gaussian quadrature for the scale-mixture representation of the GL and its projection onto the circle. A simulation study is carried out to benchmark the fitting routine against alternative estimation methods to assess its feasibility, while the projected GL model is contrasted with other popular circular distributions. A real data example is given in Supplementary Materials.

Suggested Citation

  • Geraci, Marco, 2025. "Estimation of the generalized Laplace distribution and its projection onto the circle," Statistics & Probability Letters, Elsevier, vol. 226(C).
    • Handle: RePEc:eee:stapro:v:226:y:2025:i:c:s0167715225001051
    DOI: 10.1016/j.spl.2025.110460
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    References listed on IDEAS

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    1. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309.
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    3. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
    4. Samuel Kotz & Tomaz J. Kozubowski & Krzysztof Podgórski, 2001. "The Laplace Distribution and Generalizations," Springer Books, Springer, number 978-1-4612-0173-1, December.
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