| 1. |
- Faouzi, Tarik, et al.
(författare)
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A deep look into the dagum family of isotropic covariance functions
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Annan publikation (övrigt vetenskapligt/konstnärligt)abstract
- The Dagum family of isotropic covariance functions has two parameters thatallow for decoupling of the fractal dimension and Hurst effect for Gaussianrandom fields that are stationary and isotropic over Euclidean spaces.Sufficient conditions that allow for positive definiteness in Rd of the Dagumfamily have been proposed on the basis of the fact that the Dagum familyallows for complete monotonicity under some parameter restrictions.The spectral properties of the Dagum family have been inspected to a verylimited extent only, and this paper gives insight into this direction. Specifically,we study finite and asymptotic properties of the isotropic spectral density(intended as the Hankel transform) of the Dagum model. Also, we establishsome closed forms expressions for the Dagum spectral density in terms of theFox–Wright functions. Finally, we provide asymptotic properties for such aclass of spectral densities.
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| 2. |
- Faouzi, Tarik, et al.
(författare)
-
A deep look into the Dagum family of isotropic covariance functions
- 2022
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Ingår i: Journal of Applied Probability. - Cambridge : Cambridge University Press. - 0021-9002 .- 1475-6072. ; 59:4, s. 1026-1041
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Tidskriftsartikel (refereegranskat)abstract
- The Dagum family of isotropic covariance functions has two parameters that allow fordecoupling of the fractal dimension and the Hurst effect for Gaussian random fields thatare stationary and isotropic over Euclidean spaces. Sufficient conditions that allow forpositive definiteness in $R^d$ of the Dagum family have been proposed on the basis ofthe fact that the Dagum family allows for complete monotonicity under some parameter restrictions. The spectral properties of the Dagum family have been inspected to a verylimited extent only, and this paper gives insight into this direction. Specifically, we studyfinite and asymptotic properties of the isotropic spectral density (intended as the Hankeltransform) of the Dagum model. Also, we establish some closed-form expressions forthe Dagum spectral density in terms of the Fox–Wright functions. Finally, we provideasymptotic properties for such a class of spectral densities.
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