Power law in a bounded range: Estimating the lower and upper bounds from sample data

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...

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Veröffentlicht in:The Journal of chemical physics 2023-05, Vol.158 (19)
1. Verfasser: Zhou, Huan-Xiang
Format: Artikel
Sprache:eng
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Zusammenfassung: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 involve O(N) operations. The approach centers on calculating the mean values, x̂min and x̂max, of the smallest x and the largest x in N-point samples. A fit of x̂min or x̂max 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.
ISSN:0021-9606
1089-7690
DOI:10.1063/5.0151614