The Dagum random field has been early introduced by Porcu et al. (2007).
Being Gaussian and isotropic, this random field is completely characterised by its corresponding correlation function, that additionally was shown by Mateu et al. (2007) to decouple the local and global beahaviour, that is, to treat independently the associated Haussdorff-Besicovich dimension and the Hurst effect.
Until now, there is a very important open problem related to the Dagum class of correlation functions that can be phrased as follows: find the range of parameters for which this class is permissible on any d-dimensional Euclidean space.
This problem has attracted the interest of several mathematicians and their personal communications encouraged us to investigate more deeply the problem.
The mentioned open problem finds an intimate connection with the study of the potential complete monotonicity of the Dagum function when restricted to the positive real line. In this paper, a solution of the mistery of the Dagum random field is given.