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Power Law in a Bounded Range: Estimating the Lower and Upper Bounds from Sample Data.

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Summary

Estimating bounds for power law distributions is challenging. This new O(N) method uses sample means to accurately determine lower and upper bounds, improving efficiency for analyzing scientific data.

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Area of Science:

  • Statistical physics
  • Geophysics
  • Biophysics

Background:

  • Power law distributions are prevalent across scientific disciplines, including physics, geophysics, and biology.
  • Accurate estimation of the lower and upper bounds of the independent variable (x) is crucial for these distributions.
  • Existing methods for bound estimation are computationally intensive, often requiring O(N^3) operations.

Approach:

  • A novel, computationally efficient O(N) approach for estimating bounds of power law distributions is presented.
  • The method involves calculating the mean of the minimum (x_min) and maximum (x_max) values from N-point samples.
  • Fitting x_min or x_max as a function of sample size (N) provides estimates for the lower and upper bounds, respectively.

Key Points:

  • The developed method significantly reduces computational complexity compared to previous techniques.
  • Demonstrates high accuracy and reliability in estimating bounds using synthetic datasets.
  • Offers a practical solution for analyzing datasets with power law characteristics.

Conclusions:

  • The O(N) approach provides an efficient and accurate means to estimate bounds for power law distributions.
  • This method has broad applicability in fields relying on power law analysis, such as statistical physics and geophysics.
  • Facilitates more robust analysis of complex datasets by improving bound estimation accuracy and speed.