Related papers: Return interval distribution of extreme events and…
A statistical model for describing the scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) at different scale levels the self-similarity of the distribution has…
Statistical distributions with heavy tails are ubiquitous in natural and social phenomena. Since the entries in heavy tail have disproportional significance, the knowledge of its exact shape is very important. Citations of scientific papers…
A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent close to 3. We revisit this results and use standard tests as well as develop a…
We review briefly the concepts underlying complex systems and probability distributions. The later are often taken as the first quantitative characteristics of complex systems, allowing one to detect the possible occurrence of regularities…
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:…
We investigate the statistical properties of the extreme events of the solar cycle as measured by the sunspot number. The recent advances in the methodology of the theory of extreme values is applied to the maximal extremes of the time…
We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…
We study the probability distribution of stock returns at mesoscopic time lags (return horizons) ranging from about an hour to about a month. While at shorter microscopic time lags the distribution has power-law tails, for mesoscopic times…
We empirically study the activity patterns of individual blog-posting and find significant memory effects. The memory coefficient first decays in a power law and then turns to an exponential form. Moreover, the inter-event time distribution…
We analyze a sample of bright long bursts and find that the pulses duration have a lognormal distribution while the intervals between pulses have an excess of long intervals (relative to lognormal distribution). This excess can be explained…
A length dependence of the effective mobility in the form of a power law, B ~ L^(1-1/alpha) is observed in dispersive transport in amorphous substances, with 0 < \alpha < 1. We deduce this behavior as a simple consequence of the statistical…
We investigate diffusion of excitation in one- and two-dimensional lattices with random on-site energies and deterministic long-range couplings (hopping) inversely proportional to the distance. Three regimes of diffusion are observed in…
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic…
Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…
Extreme events gain the attention of researchers due to their utmost importance in various contexts ranging from finance to climatology. This brings such recurrent events to the limelight of attention in interdisciplinary research. A…
The fluctuation scaling law has universally been observed in a wide variety of phenomena. For counting processes describing the number of events occurred during time intervals, it is expressed as a power function relationship between the…
We consider random walks on the line given by a sequence of independent identically distributed jumps belonging to the strict domain of attraction of a stable distribution, and first determine the almost sure exponential divergence rate, as…
Extreme events have an important role which is sometime catastrophic in a variety of natural phenomena including climate, earthquakes and turbulence, as well as in man-made environments like financial markets. Statistical analysis and…
The size distribution of planned and forced outages and following restoration times in power systems have been studied for almost two decades and has drawn great interest as they display heavy tails. Understanding of this phenomenon has…
We study the distribution of the occurrence of rare patterns in sufficiently mixing Gibbs random fields on the lattice $\mathbb{Z}^d$, $d\geq 2$. A typical example is the high temperature Ising model. This distribution is shown to converge…