比特币UTXO值呈重尾分布但非幂律分布：基于八个快照的Clauset-Shalizi-Newman检验
Bitcoin UTXO Values Are Heavy-Tailed but not Power-Law Distributed: A Clauset-Shalizi-Newman Test across Eight Snapshots
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中文总结 AI 辅助
本研究用Clauset-Shalizi-Newman协议检验比特币UTXO值上尾是否幂律分布，基于八个快照，发现重尾但非幂律，对数正态等分布更优。
中文摘要 AI 辅助
幂律分布常被用于描述比特币中的各类数量，其依据是双对数图的斜率。我们采用正式协议检验了这样一个论断：活跃未花费交易输出（UTXO）值的上尾是否遵循幂律分布。我们重建了2012年至2025年间八个区块高度上的精确UTXO集合，并与独立的Bitcoin Core快照进行验证，然后应用Clauset-Shalizi-Newman协议，并针对数据需求进行了三项调整：精确离散支持、在每次自助法重复中保留并重新选择多个接近并列的截断点，以及按交易进行重采样，因为同一交易的输出并非相互独立。该协议在推断前即已固定，之后的所有更改均有记录。在每个高度上，纯幂律分布均被拒绝，观测到的Kolmogorov-Smirnov距离是拟合分布产生的距离的5至40倍，且当指数低于2时，其外推预测在期望上会得到多个大于总币供应量的输出。对数正态分布、拉伸指数分布以及带有指数截断（截断点接近一千比特币）的幂律分布在每个高度上的样本内拟合均更优，作为包含幂律的分布族，其拟合优度超出在六个高度（共八个）上模拟幂律尾部所见的边际，并且在几乎所有高度上对留出交易的预测也更好。这些分布在各个高度上的排序不同，而对数正态分布与截断幂律分布仅在两个高度上存在明显差异。尾部的形状及其所持有的供应量份额随时间缓慢漂移，而输出数量增长了七十倍。该拒绝在一种能再现交易内依赖性的零假设下依然成立，这种依赖性将面板中一个异常效应量减半，但不改变任何结论。比特币UTXO值呈重尾分布，但并非幂律分布。
英文摘要
Power laws are often claimed for Bitcoin quantities from the slope of a log-log plot. We test one such claim with a formal protocol: whether the upper tail of the values of live unspent transaction outputs (UTXOs) follows a power law. We reconstruct the exact UTXO set at eight block heights from 2012 to 2025, validate it against an independent Bitcoin Core snapshot, and apply the Clauset-Shalizi-Newman protocol with three adaptations the data require: exact discrete support, several near-tied cutoffs retained and reselected in every bootstrap replicate, and resampling by transaction, because the outputs of one transaction are not independent. The protocol was fixed before inference and every later change is recorded. The pure power law is rejected at every height, with observed Kolmogorov-Smirnov distances five to forty times those the fitted law produces, and where the exponent is below 2 its extrapolation predicts, in expectation, several outputs each larger than the total coin supply. A lognormal, a stretched exponential and a power law with an exponential cutoff near a thousand bitcoin fit better in sample at every height, as families that contain the power law must, by margins that exceed those seen on simulated power-law tails at six of the eight heights, and they predict held-out transactions better at nearly every height. They rank differently from height to height, and the lognormal and the cutoff power law differ clearly at only two. The tail's shape and the share of supply it holds drifted slowly while the number of outputs grew seventy-fold. The rejection survives a null that reproduces the dependence measured within transactions, which halves the one exceptional effect size in the panel and changes no verdict. Bitcoin UTXO values are heavy-tailed but not power-law distributed.
发表机构
- Faculty of Engineering, University of Porto（波尔图大学工程学院）
- INESC TEC, Portugal（葡萄牙INESC TEC）
- Centro de Matemática, Universidade do Minho（米尼奥大学数学中心）
机构由 AI 辅助整理，请以论文原文为准。
