A deep look into the dagum family of isotropic covariance functions

• 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Probability Theory and Statistics (hsv//eng)

Keyword

Hankel Transforms; Mellin–Barnes Transforms; Spectral Theory; Positive Definite.

Mathematics/Applied Mathematics

matematik/tillämpad matematik

Publication and Content Type

vet (subject category)

ovr (subject category)