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Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions

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  • Chunsheng Ma

Abstract

In terms of the two-parameter Mittag-Leffler function with specified parameters, this paper introduces the Mittag-Leffler vector random field through its finite-dimensional characteristic functions, which is essentially an elliptically contoured one and reduces to a Gaussian one when the two parameters of the Mittag-Leffler function equal 1. Having second-order moments, a Mittag-Leffler vector random field is characterized by its mean function and its covariance matrix function, just like a Gaussian one. In particular, we construct direct and cross covariances of Mittag-Leffler type for such vector random fields. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Chunsheng Ma, 2013. "Mittag-Leffler vector random fields with Mittag-Leffler direct and cross covariance functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 941-958, October.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:5:p:941-958
    DOI: 10.1007/s10463-013-0398-9
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    1. Yasuhiro Fujita, 1993. "A generalization of the results of Pillai," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(2), pages 361-365, June.
    2. Chunsheng Ma, 2005. "Semiparametric spatio-temporal covariance models with the ARMA temporal margin," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(2), pages 221-233, June.
    3. R. Pillai, 1990. "On Mittag-Leffler functions and related distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 42(1), pages 157-161, March.
    4. Marco Minozzo, 2011. "On the existence of some skew normal stationary processes," Working Papers 20/2011, University of Verona, Department of Economics.
    5. Ma, Chunsheng, 2013. "K-distributed vector random fields in space and time," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1143-1150.
    6. Kleiber, William & Nychka, Douglas, 2012. "Nonstationary modeling for multivariate spatial processes," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 76-91.
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    Cited by:

    1. Ma, Chunsheng, 2021. "Hyperbolic cosine ratio and hyperbolic sine ratio random fields," Statistics & Probability Letters, Elsevier, vol. 179(C).
    2. Lu, Tianshi & Du, Juan & Ma, Chunsheng, 2022. "Stochastic comparison for elliptically contoured random fields," Statistics & Probability Letters, Elsevier, vol. 189(C).
    3. Moreno Bevilacqua & Ronny Vallejos & Daira Velandia, 2015. "Assessing the significance of the correlation between the components of a bivariate Gaussian random field," Environmetrics, John Wiley & Sons, Ltd., vol. 26(8), pages 545-556, December.

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