2023/03/23 by Zhou, Huan-Xiang
#Biological Physics (physics.bio-ph) #Biomolecules (q-bio.BM) #Chemical Physics (physics.chem-ph) #Data Analysis #FOS: Biological sciences #FOS: Physical sciences #Geophysics (physics.geo-ph) #Statistics and Probability (physics.data-an)
paper · doi:10.48550/arxiv.2303.13456
Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and in many cases also an upper bound. Estimating these bounds from sample data is notoriously difficult, with a recent method involving O(N3) operations, where N denotes sample size. Here I develop an approach for estimating the lower and upper bounds that involves O(N) operations. The approach centers on calculating the mean values, xmin and xmax, of the smallest x and the largest x in N-point samples. A fit of xmin or xmax as a function of N yields the estimate for the lower or upper bound. Application to synthetic data demonstrates the accuracy and reliability of this approach.