# The Dagum family of isotropic correlation functions

@article{Berg2008TheDF,
title={The Dagum family of isotropic correlation functions},
author={Christian Berg and Jorge Mateu and Emilio Porcu},
journal={Bernoulli},
year={2008},
volume={14},
pages={1134-1149}
}
• Published 3 May 2007
• Mathematics
• Bernoulli
A function $\rho:[0,\infty)\to(0,1]$ is a completely monotonic function if and only if $\rho(\Vert\mathbf{x}\Vert^2)$ is positive definite on $\mathbb{R}^d$ 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…

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