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Multivariate generalized Laplace distribution and related random fields

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  • Kozubowski, Tomasz J.
  • Podgórski, Krzysztof
  • Rychlik, Igor

Abstract

Multivariate Laplace distribution is an important stochastic model that accounts for asymmetry and heavier than Gaussian tails, while still ensuring the existence of the second moments. A Lévy process based on this multivariate infinitely divisible distribution is known as Laplace motion, and its marginal distributions are multivariate generalized Laplace laws. We review their basic properties and discuss a construction of a class of moving average vector processes driven by multivariate Laplace motion. These stochastic models extend to vector fields, which are multivariate both in the argument and the value. They provide an attractive alternative to those based on Gaussianity, in presence of asymmetry and heavy tails in empirical data. An example from engineering shows modeling potential of this construction.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:113:y:2013:i:c:p:59-72
    DOI: 10.1016/j.jmva.2012.02.010
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    References listed on IDEAS

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    1. Sun, Lu, 2001. "Computer simulation and field measurement of dynamic pavement loading," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 56(3), pages 297-313.
    2. Olcay Arslan, 2010. "An alternative multivariate skew Laplace distribution: properties and estimation," Statistical Papers, Springer, vol. 51(4), pages 865-887, December.
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    2. Hušková, Marie & Meintanis, Simos G. & Pretorius, Charl, 2020. "Tests for validity of the semiparametric heteroskedastic transformation model," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    3. Nam-Hwui Kim & Ryan Browne, 2019. "Subspace clustering for the finite mixture of generalized hyperbolic distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(3), pages 641-661, September.
    4. Loperfido, Nicola, 2024. "The skewness of mean–variance normal mixtures," Journal of Multivariate Analysis, Elsevier, vol. 199(C).
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    6. Marc Hallin & Simos Meintanis & Klaus Nordhausen, 2024. "Consistent Distribution–Free Affine–Invariant Tests for the Validity of Independent Component Models," Working Papers ECARES 2024-04, ULB -- Universite Libre de Bruxelles.
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    11. Taras Bodnar & Stepan Mazur & Nestor Parolya, 2019. "Central limit theorems for functionals of large sample covariance matrix and mean vector in matrix‐variate location mixture of normal distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 46(2), pages 636-660, June.
    12. Marie Hušková & Simos G. Meintanis & Charl Pretorius, 2022. "Tests for heteroskedasticity in transformation models," Statistical Papers, Springer, vol. 63(4), pages 1013-1049, August.
    13. Hongyan Fang & Saisai Ding & Xiaoqin Li & Wenzhi Yang, 2020. "Asymptotic Approximations of Ratio Moments Based on Dependent Sequences," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    14. Chen, Feifei & Jiménez–Gamero, M. Dolores & Meintanis, Simos & Zhu, Lixing, 2022. "A general Monte Carlo method for multivariate goodness–of–fit testing applied to elliptical families," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
    15. Mahmoudian, Behzad, 2018. "On the existence of some skew-Gaussian random field models," Statistics & Probability Letters, Elsevier, vol. 137(C), pages 331-335.
    16. Mattei, Pierre-Alexandre, 2017. "Multiplying a Gaussian matrix by a Gaussian vector," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 67-70.
    17. Jevtić, Petar & Marena, Marina & Semeraro, Patrizia, 2017. "A note on Marked Point Processes and multivariate subordination," Statistics & Probability Letters, Elsevier, vol. 122(C), pages 162-167.
    18. Quessy, Jean-François & Durocher, Martin, 2019. "The class of copulas arising from squared distributions: Properties and inference," Econometrics and Statistics, Elsevier, vol. 12(C), pages 148-166.
    19. Chen, Feifei & Meintanis, Simos G. & Zhu, Lixing, 2019. "On some characterizations and multidimensional criteria for testing homogeneity, symmetry and independence," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 125-144.
    20. Maria Grazia Zoia & Gianmarco Vacca & Laura Barbieri, 2020. "Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions," Risks, MDPI, vol. 8(4), pages 1-21, November.
    21. Maume-Deschamps, V. & Rullière, D. & Usseglio-Carleve, A., 2017. "Quantile predictions for elliptical random fields," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 1-17.

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