Analysis of power-law exponents by maximum-likelihood maps

Abstract

Maximum-likelihood exponent maps have been studied as a technique to increase the understanding and improve the fit of power-law exponents to experimental and numerical simulation data, especially when they exhibit both upper and lower cut-offs. The use of the technique is tested by analyzing seismological data, acoustic emission data and avalanches in numerical simulations of the 3D-Random Field Ising model. In the different examples we discuss the nature of the deviations observed in the exponent maps and some relevant conclusions are drawn for the physics behind each phenomenon.

15 pages, 14 figures

References in corpus (7)

• Power-law distributions in empirical data
• Statistical Models of Fracture
• Parameter estimation for power-law distributions by maximum likelihood methods
• Universality of rain event size distributions
• Driving-induced crossover: from classical criticality to self-organized criticality
• Unexpected universality in static and dynamic avalanches
• Random Field Potts model with dipolar-like interactions: hysteresis, avalanches and microstructure

Cited by in corpus (6)

• Plastic yielding and deformation bursts in the presence of disorder from coherent precipitates
• Modelling avalanches in martensites
• Tail of the distribution of fatalities in epidemics
• Striation lines in intermittent fatigue crack growth in an Al alloy
• Punctuated evolution of influenza virus hemagglutinin (A/H1N1) under opposing migration and vaccination pressures
• Scientific comment on "Tail risk of contagious diseases"