相关论文: Statistical Distributions of Earthquake Numbers: C…
We study the distributions of earthquake numbers in two global catalogs: Global Centroid-Moment Tensor and Preliminary Determinations of Epicenters. These distributions are required to develop the number test for forecasts of future seismic…
Rank-ordering statistics provides a perspective on the rare, largest elements of a population, whereas the statistics of cumulative distributions are dominated by the more numerous small events. The exponent of a power law distribution can…
Frequency-magnitude distributions, and their associated uncertainties, are of key importance in statistical seismology. When fitting these distributions, the assumption of Gaussian residuals is invalid since event numbers are both discrete…
Bayesian neural networks (BNN) are the probabilistic model that combines the strengths of both neural network (NN) and stochastic processes. As a result, BNN can combat overfitting and perform well in applications where data is limited.…
Multiplicity distributions $P(N)$ measured in multiparticle production processes are most frequently described by the Negative Binomial Distribution (NBD). However, with increasing collision energy some systematic discrepancies become more…
The seemingly disjoint problems of count and mixture modeling are united under the negative binomial (NB) process. A gamma process is employed to model the rate measure of a Poisson process, whose normalization provides a random probability…
The statistics of natural catastrophes contains very counter-intuitive results. Using earthquakes as a working example, we show that the energy radiated by such events follows a power-law or Pareto distribution. This means, in theory, that…
The distribution of inter-occurrence time between seismic events is a quantity of great interest in seismic risk assessment. We evaluate this distribution for different models of earthquakes occurrence and follow two distinct approaches:…
Standard approaches to forecasting the weekly number of earthquakes on a spatial grid rely on the Poisson distribution with a single global dispersion assumption. We show that this assumption is systematically violated in seismic data from…
The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…
We propose a branching process based on a dynamical scaling hypothesis relating time and mass. In the context of earthquake occurrence, we show that experimental power laws in size and time distribution naturally originate solely from this…
Numerical simulation of seismicity has been successfully developed and used for the two last decades. Presently, the general theory of modeling and the progress in computational techniques provide wide options for simulation of seismic and…
We present the "condensation" method that exploits the heterogeneity of the probability distribution functions (PDF) of event locations to improve the spatial information content of seismic catalogs. The method reduces the size of seismic…
We review the present status of our research and understanding regarding the dynamics and the statistical properties of earthquakes, mainly from a statistical physical viewpoint. Emphasis is put both on the physics of friction and fracture,…
Fluctuations in the occurrence of large, disastrous earthquakes are important for the study of deviations from the regular behavior of earthquakes. In this study, to assist in our understanding of the irregular behavior of earthquake…
In this paper, we used the Global Catalog of the National Earthquake Information Center US Geological Survey (NEIC USGS) for analysis of the magnitude-frequency distribution of earthquakes. We selected the unimodal part of the distribution…
The generalized negative binomial distribution (GNB) is a new flexible family of discrete distributions that are mixed Poisson laws with the mixing generalized gamma (GG) distributions. This family of discrete distributions is very wide and…
In our paper published earlier we discussed forecasts of earthquake focal mechanism and ways to test the forecast efficiency. Several verification methods were proposed, but they were based on ad-hoc, empirical assumptions, thus their…
This chapter introduces the fracture nucleation process, their (extreme) statistics in disordered solids, in fiber bundle models, and in the two fractal overlap models of earthquake.
The general theory of the branching processes is used for establishing the relation between the parameters $k$ and $\bar n$ of the negative binomial distribution. This relation gives the possibility to describe the overall data on…