  Complex biological networks, comprising metabolic reactions, gene
interactions, and protein interactions, often exhibit scale-free
characteristics with power-law degree distributions. However, empirical studies
have revealed discrepancies between observed biological network data and ideal
power-law fits, highlighting the need for improved modeling approaches. To
address this challenge, we propose a novel family of distributions, building
upon the baseline Burr distribution. Specifically, we introduce the compounded
Burr (CBurr) distribution, derived from a continuous probability distribution
family, enabling flexible and efficient modeling of node degree distributions
in biological networks. This study comprehensively investigates the general
properties of the CBurr distribution, focusing on parameter estimation using
the maximum likelihood method. Subsequently, we apply the CBurr distribution
model to large-scale biological network data, aiming to evaluate its efficacy
in fitting the entire range of node degree distributions, surpassing
conventional power-law distributions and other benchmarks. Through extensive
data analysis and graphical illustrations, we demonstrate that the CBurr
distribution exhibits superior modeling capabilities compared to traditional
power-law distributions. This novel distribution model holds great promise for
accurately capturing the complex nature of biological networks and advancing
our understanding of their underlying mechanisms.
