Power Law Distribution: Method of Multi-scale Inferential Statistics

Power law distribution appears in several scientific fields such as physics, earth science, economics, social science and many others. This paper illustrates new practical criteria for inferential statistics involving power law and, namely for estimation of power law distribution exponent and its confidence interval. To calculate this latter interval new expressions, in closed form, are derived. This methodology has been compared with classical least squares method and that of maximum likelihood, showing that it provides a more efficient estimator for power law exponent. In order to describe this criterion by means of a case study, it has been applied to statistical multi-scale analysis of fracture networks in a petroleum reservoir analogue, nevertheless it can be applied in several contexts involving scale free distributions.

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