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A Multivariate and Asymmetric Generalization of Laplace Distribution

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  • Tomasz J. Kozubowski

    (The University of Tennessee at Chattanooga)

  • Krzysztof Podgórski

    (Indiana University — Purdue University)

Abstract

Summary Consider a sum of independent and identically distributed random vectors with finite second moments, where the number of terms has a geometric distribution independent of the summands. We show that the class of limiting distributions of such random sums, as the number of terms converges to infinity, consists of multivariate asymmetric distributions that are natural generalizations of univariate Laplace laws. We call these limits multivariate asymmetric Laplace laws. We give an explicit form of their multidimensional densities and show representations that effectively facilitate computer simulation of variates from this class. We also discuss the relation to other formerly considered classes of distributions containing Laplace laws.

Suggested Citation

  • Tomasz J. Kozubowski & Krzysztof Podgórski, 2000. "A Multivariate and Asymmetric Generalization of Laplace Distribution," Computational Statistics, Springer, vol. 15(4), pages 531-540, December.
    • Handle: RePEc:spr:compst:v:15:y:2000:i:4:d:10.1007_pl00022717
    DOI: 10.1007/PL00022717
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    References listed on IDEAS

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    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
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    3. Anderson, Dale N., 1992. "A multivariate Linnik distribution," Statistics & Probability Letters, Elsevier, vol. 14(4), pages 333-336, July.
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    Cited by:

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    2. Tsionas, Mike G. & Assaf, A. George & Andrikopoulos, Athanasios, 2020. "Quantile stochastic frontier models with endogeneity," Economics Letters, Elsevier, vol. 188(C).
    3. Wang, Yun & Xu, Houhua & Zou, Runmin & Zhang, Lingjun & Zhang, Fan, 2022. "A deep asymmetric Laplace neural network for deterministic and probabilistic wind power forecasting," Renewable Energy, Elsevier, vol. 196(C), pages 497-517.
    4. He, J.Y. & Chan, P.W. & Li, Q.S. & Lee, C.W., 2022. "Characterizing coastal wind energy resources based on sodar and microwave radiometer observations," Renewable and Sustainable Energy Reviews, Elsevier, vol. 163(C).
    5. Zozor, S. & Vignat, C., 2007. "On classes of non-Gaussian asymptotic minimizers in entropic uncertainty principles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 499-517.
    6. Guney, Yesim & Arslan, Olcay & Yavuz, Fulya Gokalp, 2022. "Robust estimation in multivariate heteroscedastic regression models with autoregressive covariance structures using EM algorithm," Journal of Multivariate Analysis, Elsevier, vol. 191(C).
    7. Wan-Lun Wang & Ahad Jamalizadeh & Tsung-I Lin, 2020. "Finite mixtures of multivariate scale-shape mixtures of skew-normal distributions," Statistical Papers, Springer, vol. 61(6), pages 2643-2670, December.
    8. Shi, Jianhong & Bai, Xiuqin & Song, Weixing, 2022. "Tweedie-type formulae for a multivariate Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 183(C).
    9. Kozubowski, Tomasz J. & Meerschaert, Mark M. & Panorska, Anna K. & Scheffler, Hans-Peter, 2005. "Operator geometric stable laws," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 298-323, February.

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