Power laws have been found to describe a wide variety of natural (physical, biological, astronomic, meteorological, geological) and man-made (social, financial, computational) phenomena over a wide range of magnitudes, although their underlying mechanisms are not always clear. In statistics, power law distribution is often found to fit data exceptionally well when the normal (Gaussian) distribution fails. Nevertheless, predicting power law phenomena is notoriously difficult because some of its idiosyncratic properties such as lack of well-defined average value, and potentially unbounded variance. TPL (Taylor power law), a power law first discovered to characterize the spatial and/or temporal distribution of biological populations and recently extended to describe the spatiotemporal heterogeneities (distributions) of human microbiomes and other natural and artificial systems such as fitness distribution in computational (artificial) intelligence. The power law with exponential cutoff (PLEC) is a variant of power-law function that tapers off the exponential growth of power-law function ultimately and can be particularly useful for certain predictive problems such as biodiversity estimation and turning-point prediction for COVID-19 infection/fatality. Here, we propose coupling (integration) of TPL and PLEC to offer improved prediction quality of certain power-law phenomena. The coupling takes advantages of variance prediction using TPL and the asymptote estimation using PLEC and delivers confidence interval for the asymptote. We demonstrate the integrated approach to the estimation of potential (dark) biodiversity and turning point of COVID-19 fatality. We expect this integrative approach should have wide applications given the duel relationship between power law and normal statistical distributions.
翻译:电法的分布往往被认为在正常(Gausian)分布失败时非常符合数据。然而,预测电法现象却十分困难,因为其一些特异性性特征,如缺乏明确界定的平均价值和潜在的未受限制的估算值。TPL(Taylor 电力法),一种首次发现的权力法,以描述生物种群的空间和/或时间分布特征,而最近又扩展至描述人类微生物和其他自然和人工系统在空间和/或时间差异方面的差异性(分布),如正常(Gausian)分布不力时,往往发现权力法分配非常适合数据。不过,预测权力法现象是众所周知的,因为一些特异性法方法,例如缺乏明确界定的平均价值,而且可能无法预测。TPL(Tylororal 电力法),一种首次发现的权力法法,首先为生物种群的空间和/或时间分布法,首次发现这种生物种群的空间和时间分布特征,而最近又扩展到描述人类微生物-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏循环预测法。我们使用Tel-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏循环的预测法,将某些病毒-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏关系-肝脏-肝脏关系-肝脏关系-肝脏关系-肝脏-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏关系-肝脏-肝脏关系-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏-肝脏关系-肝脏关系-肝脏关系-肝脏-肝脏-肝脏-肝脏-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝关系-肝-