A DEEP LOOK INTO THE DAGUM FAMILY OF ISOTROPIC COVARIANCE FUNCTIONS

Tarik Faouzi, Emilio Porcu, Igor Kondrashuk, Anatoliy Malyarenko

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

The Dagum family of isotropic covariance functions has two parameters that allow for decoupling of the fractal dimension and the Hurst effect for Gaussian random fields that are stationary and isotropic over Euclidean spaces. Sufficient conditions that allow for positive definiteness in Rd of the Dagum family have been proposed on the basis of the 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 very limited 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 establish some closed-form expressions for the Dagum spectral density in terms of the Fox–Wright functions. Finally, we provide asymptotic properties for such a class of spectral densities.

Original languageBritish English
Pages (from-to)1026-1041
Number of pages16
JournalJournal of Applied Probability
Volume59
Issue number4
DOIs
StatePublished - 18 Dec 2022

Keywords

  • Hankel transforms
  • Mellin–Barnes transforms
  • positive definite
  • spectral theory

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