Results of avalanche-analysis for thresholded stochastic processes.

Results of avalanche-analysis for avalanche-sizes analytically determined for four stochastic processes. Table headers are the same as in Table 1. The estimated power-law is large because we considered the tail of the distribution, and since the data present an exponential trend, the estimated power-law exponent becomes larger when thresholds are high. Even if the p-value is high, the fit is not realistic and the does not hold for larger intervals. We do not use the log-likelihood ratio since it is defined for samples and does not really make sense for distributions.

针对四种随机过程（stochastic process）的雪崩尺寸开展解析推导后得到的雪崩分析结果。本次分析的表格表头与表1完全一致。本次估算得到的幂律（power-law）数值偏大，原因在于我们选取了分布的尾部进行分析；同时由于数据呈现指数趋势，当阈值升高时，估算得到的幂律指数也会随之增大。即便p值较高，该拟合结果也并不符合实际，且在更大的区间范围内不再成立。我们未采用对数似然比（log-likelihood ratio），因为该指标仅针对样本定义，对于分布而言并无实际意义。