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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 family allowsfor complete monotonicity under some parameter restrictions. The spectralproperties of the Dagum family have been inspected to a very limited extentonly, and this paper gives insight into this direction. Specifically, we studyfinite and asymptotic properties of the isotropic spectral density (intended asthe Hankel transform) of the Dagum model. Also, we establish some closed formsexpressions for the Dagum spectral density in terms of the Fox{Wrightfunctions. Finally, we provide asymptotic properties for such a class ofspectral densities.

A deep look into the Dagum family of isotropic covariance functions