q-exponential, Weibull, and q-Weibull distributions: an empirical analysis

Abstract

In a comparative study, the q-exponential and Weibull distributions are employed to investigate frequency distributions of basketball baskets, cyclone victims, brand-name drugs by retail sales, and highway length. In order to analyze the intermediate cases, a distribution, the q-Weibull one, which interpolates the q-exponential and Weibull ones, is introduced. It is verified that the basketball baskets distribution is well described by a q-exponential, whereas the cyclone victims and brand-name drugs by retail sales ones are better adjusted by a Weibull distribution. On the other hand, for highway length the q-exponential and Weibull distributions do not give satisfactory adjustment, being necessary to employ the q-Weibull distribution. Furthermore, the introduction of this interpolating distribution gives an illumination from the point of view of the stretched exponential against inverse power law (q-exponential with q > 1) controversy.

6 pages, Latex. To appear in Physica A

References in corpus (9)

• How Popular is Your Paper? An Empirical Study of the Citation Distribution
• Stretched exponential distributions in Nature and Economy: ``Fat tails'' with characteristic scales
• Power Laws in Solar Flares: Self-Organized Criticality or Turbulence?
• Beyond the Zipf-Mandelbrot law in quantitative linguistics
• Modeling Urban Growth Patterns with Correlated Percolation
• Are citations of scientific papers a case of nonextensivity ?
• Nonlinear equation for anomalous diffusion: unified power-law and stretched exponential exact solution
• q-Exponential Distribution in Urban Agglomeration
• Regularities in football goal distributions

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