powerlaw: a Python package for analysis of heavy-tailed distributions

powerlaw: a Python package for analysis of heavy-tailed distributions

31 Jan 2014 | Jeff Alstott, Ed Bullmore, Dietmar Plenz
The powerlaw Python package is designed to facilitate the analysis of heavy-tailed distributions, which are theoretically interesting and frequently observed in empirical data. The package provides an easy-to-use interface for fitting power law distributions and performing statistical analysis. It supports a wide range of probability distributions and subtypes, and is extensible and maintainable. The package is publicly available and can be easily installed via pip. Power law distributions have the form p(x) ∝ x^(-α), and are characterized by heavy tails, meaning that the right tails of the distributions contain a significant amount of probability. These distributions are scale-free, meaning that all values are expected to occur without a characteristic size or scale. Power laws have been identified in various fields, including astrophysics, linguistics, and neuroscience. Fitting a power law distribution to empirical data requires careful consideration of the data's characteristics and the appropriate statistical methods. The powerlaw package includes functions for visualizing, fitting, and comparing distributions. It supports the calculation of probability density functions (PDFs), cumulative distribution functions (CDFs), and complementary cumulative distribution functions (CCDFs). The package also includes methods for identifying the scaling range of the data and comparing the goodness of fit between different distributions. The package supports both continuous and discrete data, and includes methods for handling discrete distributions. It also includes functions for generating simulated data from theoretical distributions, which can be used to validate the accuracy of the fitting software. The powerlaw package is designed to be user-friendly and efficient, with a focus on ease of use and extensibility. It is supported by a range of open-source packages, including NumPy, SciPy, and matplotlib. The package is available on PyPI and GitHub, and is regularly updated to include new features and improvements.The powerlaw Python package is designed to facilitate the analysis of heavy-tailed distributions, which are theoretically interesting and frequently observed in empirical data. The package provides an easy-to-use interface for fitting power law distributions and performing statistical analysis. It supports a wide range of probability distributions and subtypes, and is extensible and maintainable. The package is publicly available and can be easily installed via pip. Power law distributions have the form p(x) ∝ x^(-α), and are characterized by heavy tails, meaning that the right tails of the distributions contain a significant amount of probability. These distributions are scale-free, meaning that all values are expected to occur without a characteristic size or scale. Power laws have been identified in various fields, including astrophysics, linguistics, and neuroscience. Fitting a power law distribution to empirical data requires careful consideration of the data's characteristics and the appropriate statistical methods. The powerlaw package includes functions for visualizing, fitting, and comparing distributions. It supports the calculation of probability density functions (PDFs), cumulative distribution functions (CDFs), and complementary cumulative distribution functions (CCDFs). The package also includes methods for identifying the scaling range of the data and comparing the goodness of fit between different distributions. The package supports both continuous and discrete data, and includes methods for handling discrete distributions. It also includes functions for generating simulated data from theoretical distributions, which can be used to validate the accuracy of the fitting software. The powerlaw package is designed to be user-friendly and efficient, with a focus on ease of use and extensibility. It is supported by a range of open-source packages, including NumPy, SciPy, and matplotlib. The package is available on PyPI and GitHub, and is regularly updated to include new features and improvements.
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