Parameter estimation for power-law distributions by maximum likelihood methods
By Heiko Bauke. 2007
207 citations recorded by the source corpus.
Abstract.Distributions following a power-law are an ubiquitous phenomenon. Methods for determining the exponent of a power-law tail by graphical means are often used in practice but are intrinsically unreliable. Maximum likelihood estimators for the exponent are a mathematically sound alternative to graphical methods.
Subfields: Condensed Matter Physics, Economics and Econometrics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/9abfd5555ae5fca02d1d63c3edb63d9d3efeec0d
How researchers see this paper
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In Condensed Matter Physics
- Michael W. Mahoney
- Á. Corral
- Mark Newman
- Aaron Clauset
- Anna Deluca
- Tao Jin
- Charles H. Martin
- Robert J. Barro
In Economics and Econometrics
- Michael W. Mahoney
- Charles H. Martin
- Aaron Clauset
- Á. Corral
- Anna Deluca
- Tao Jin
- Robert J. Barro
- Mark Newman
In Statistical and Nonlinear Physics
- Michael W. Mahoney
- Charles H. Martin
- Aaron Clauset
- Mark Newman
- Santo Fortunato
- Jure Leskovec
- Á. Corral
- Anna Deluca
Citations in the corpus
- Implicit Self-Regularization in Deep Neural Networks: Evidence from Random Matrix Theory and Implications for Learning (2018, background): “Generally speaking, fitting a PL has many subtleties, most beyond the scope of this paper [33, 55, 91, 100, 16, 73, 35, 2, 145, 58].”
- Fitting and goodness-of-fit test of non-truncated and truncated power-law distributions (2012, methodology): “This property is called asymptotical efficiency (Bauke, 2007; White et al., 2008).”
- On the Size Distribution of Macroeconomic Disasters (2009, methodology): “A more common method to estimate α is maximum likelihood or MLE—see, for example, Howell (2004) and Bauke (2007).”
- Power-Law Distributions in Empirical Data (2007, background): “The standard approach in such cases is instead to maximize the marginal likelihood, i.e., the likelihood of the data given the number of model parameters, but with the model parameters themselves integrated out.”
- Firm Size Distortions and the Productivity Distribution: Evidence from France (2013, unknown): “1 Empirical Model Recall that our starting point is the pdf of ∗, which is, according to the theory, given by equation (13).”