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.

翻译：由代谢反应、基因相互作用和蛋白质相互作用构成的复杂生物网络，通常表现出具有幂律度分布的无标度特性。然而，实证研究揭示了观测到的生物网络数据与理想的幂律拟合之间存在差异，这凸显了改进建模方法的必要性。为应对这一挑战，我们在基准Burr分布的基础上，提出了一族新的分布。具体而言，我们引入了复合Burr（CBurr）分布，它源自一个连续概率分布族，能够灵活高效地对生物网络中的节点度分布进行建模。本研究全面探讨了CBurr分布的一般性质，重点在于使用最大似然法进行参数估计。随后，我们将CBurr分布模型应用于大规模生物网络数据，旨在评估其在拟合整个节点度分布范围上的效能，以超越传统的幂律分布及其他基准模型。通过广泛的数据分析和图形化说明，我们证明了CBurr分布相较于传统幂律分布展现出更优越的建模能力。这一新颖的分布模型在精确捕捉生物网络的复杂本质以及增进我们对其潜在机制的理解方面具有巨大潜力。