Modified Lomax model: a heavy-tailed distribution for fitting large-scale real-world complex networks

Abstract

Real-world networks are generally claimed to be scale-free, meaning that the degree distributions follow the classical power-law, at least asymptotically. Yet, closer observation shows that the classical power-law distribution is often inadequate to meet the data characteristics due to the existence of a clearly identifiable non-linearity in the entire degree distribution in the log-log scale. The present paper proposes a new variant of the popular heavy-tailed Lomax distribution which we named as the Modified Lomax (MLM) distribution that can efficiently capture the crucial aspect of heavy-tailed behavior of the entire degree distribution of real-world complex networks. The proposed MLM model, derived from a hierarchical family of Lomax distributions, can efficiently fit the entire degree distribution of real-world networks without removing lower degree nodes as opposed to the classical power-law based fitting. The MLM distribution belongs to the maximum domain of attraction of the Frechet distribution and is right tail equivalent to Pareto distribution. Various statistical properties including characteristics of the maximum likelihood estimates and asymptotic distributions have also been derived for the proposed MLM model. Finally, the effectiveness of the proposed MLM model is demonstrated through rigorous experiments over fifty real-world complex networks from diverse applied domains.