Penalized KS method to fit data sets with power law distribution over a bounded subinterval

Fatih Olmez, Peter R. Kramer, John Fricks, Deena R. Schmidt, Janet Best

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


We develop a variation of a Kolmogorov-Smirnov (KS) method for estimating a power law region, including its lower and upper bounds, of the probability density in a set of data which can be modelled as a continuous random sample. Our main innovation is to stabilize the estimation of the bounds of the power law region by introducing an adaptive penalization term involving the logarithmic length of the interval when minimizing the Kolmogorov-Smirnov distance between the random sample and the power law fit over various candidate intervals. We show through simulation studies that an adaptively penalized Kolmogorov-Smirnov (apKS) method improves the estimation of the power law interval on random samples from various theoretical probability distributions. Variability in the estimation of the bounds can be further reduced when the apKS method is applied to subsamples of the original random sample, and the subsample estimates are averaged to yield a final estimate.

Original languageEnglish (US)
Pages (from-to)1524-1563
Number of pages40
JournalJournal of Statistical Computation and Simulation
Issue number8
StatePublished - 2021


  • KS
  • Truncated power law
  • bounded power law
  • penalization
  • power law interval
  • validation

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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