Working Paper Article Version 1 This version is not peer-reviewed

Modeling the Degree Distributions of Heavy-Tailed Networks by Generalized Lomax Models

Version 1 : Received: 5 June 2020 / Approved: 7 June 2020 / Online: 7 June 2020 (09:11:22 CEST)

How to cite: Chakraborty, T.; Chattopadhyay, S.; Das, S. Modeling the Degree Distributions of Heavy-Tailed Networks by Generalized Lomax Models. Preprints 2020, 2020060071 Chakraborty, T.; Chattopadhyay, S.; Das, S. Modeling the Degree Distributions of Heavy-Tailed Networks by Generalized Lomax Models. Preprints 2020, 2020060071

Abstract

Heavy-tailed networks are often characterized in the literature of complex networks by their degree distribution’s similarity to a power-law. However, most of these heavy-tailed real-world networks do not follow power-law degree distributions. In many applications, the scale-free nature of these networks is irrelevant so long as the system possesses hubs. A closer observation shows that the classical power-law distribution is often inadequate to meet the data characteristics. This is due to the existence of an identifiable non-linearity in the entire degree distribution in a log-log scale. In this paper, we propose a new class of heavy-tailed probability distributions, which we call “generalized Lomax model”. In the generalized Lomax model, we model the tail-index or the shape parameter of the Lomax distribution using a nonlinear function, which depends on the data and two parameters. This new class of distributions will be useful for modeling heavy-tailed network data sets in the whole range. The basic structural properties of the proposed model, including its extreme value and inferential properties, are presented. The newly derived generalized Lomax models belong to the maximum domain of attractions of the Frechet distribution and are right tail equivalent to Pareto distribution. The closeness of the generalized Lomax models with that of various life distributions is investigated. Experimental analysis suggests that the proposed distributions can better model largescale, heavy-tailed network data sets in the whole range compared to current state-of-the-art models.

Subject Areas

Heavy-tailed networks; tail-index modeling; Lomax distribution; parameter estimation; extreme value properties

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.