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• W3100276384 abstract "A function $ρ:[0, ∞)→(0, 1]$ is a completely monotonic function if and only if $ρ(‖mathbf{x}‖^2)$ is positive definite on $ℝ^d$ for all $d$ and thus it represents the correlation function of a weakly stationary and isotropic Gaussian random field. Radial positive definite functions are also of importance as they represent characteristic functions of spherically symmetric probability distributions. In this paper, we analyze the function $$rho(beta ,gamma)(x)=1-biggl(frac{x^{beta}}{1+x^{beta}}biggr)^{gamma},qquad xge 0, beta,gamma>0,$$ called the Dagum function, and show those ranges for which this function is completely monotonic, that is, positive definite, on any $d$-dimensional Euclidean space. Important relations arise with other families of completely monotonic and logarithmically completely monotonic functions." @default.
• W3100276384 created "2020-11-23" @default.
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• W3100276384 date "2008-11-01" @default.
• W3100276384 modified "2023-10-02" @default.
• W3100276384 title "The Dagum family of isotropic correlation functions" @default.
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• W3100276384 doi "https://doi.org/10.3150/08-bej139" @default.
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