A deep look into the Dagum family of isotropic covariance functions

• 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.

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

ref (subject category)

art (subject category)