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Licence: CC BY: Creative Commons Attribution 4.0 International License
Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
}
TY - JOUR
T1 - Degree distributions in networks:
T2 - beyond the power law
AU - Lee, Clement
AU - Eastoe, Emma
AU - Farrell, Aiden
PY - 2024/11/30
Y1 - 2024/11/30
N2 - The power law is useful in describing count phenomena such as network degreesand word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been criticisms of the power law, for example that a threshold needs to be pre-selected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modelling framework that combines two different generalisations of the power law, namely the generalised Pareto distribution and the Zipf-polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate.
AB - The power law is useful in describing count phenomena such as network degreesand word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been criticisms of the power law, for example that a threshold needs to be pre-selected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modelling framework that combines two different generalisations of the power law, namely the generalised Pareto distribution and the Zipf-polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate.
UR - https://doi.org/10.48550/arXiv.2008.03073
U2 - 10.1111/stan.12355
DO - 10.1111/stan.12355
M3 - Journal article
VL - 78
SP - 702
EP - 718
JO - Statistica Neerlandica
JF - Statistica Neerlandica
SN - 0039-0402
IS - 4
ER -