Related papers: Finite-Size Effects on Return Interval Distributio…
The fracture strength distribution of materials is often described in terms of the Weibull law which can be derived by using extreme value statistics if elastic interactions are ignored. Here, we consider explicitly the interplay between…
Weibull distribution is widely used in modelling health data. However, its lack of sufficient tail flexibility often results in poor fit in extreme events. We proposed another three-parameter extension of the Weibull distribution with…
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…
Recent progress in nanotechnology enables us to utilize the elastic strain engineering, the emerging technology capable of controlling the physio-chemical properties of materials via externally-imposed elastic strains, for hard materials.…
We report a novel critical behavior in the breakdown of an equal load sharing fiber bundle model at a dispersion $\delta_c$ of the breaking threshold of the fibers. For $\delta < \delta_c$, there is a finite probability $P_b$, that…
We investigate how the macroscopic response and the size scaling of the ultimate strength of materials change when their local strength is sampled from a fat-tailed distribution and the degree of disorder is varied in a broad range. Using…
In reliability and life data analysis, the Weibull distribution is widely used to accommodate more data characteristics by changing the values of the parameters. We frequently observe many zeros or close to zero data points in reliability…
We study extremal statistics and return intervals in stationary long-range correlated sequences for which the underlying probability density function is bounded and uniform. The extremal statistics we consider e.g., maximum relative to…
The current understanding of the earthquake interevent times distribution (ITD) is incomplete. The Weibull distribution is often used to model the earthquake ITD. We link the earthquake ITD on single faults with the Earth's crustal shear…
We study fracture processes within a stochastic fiber-bundle model where it is assumed that after the failure of a fiber, each intact fiber obtains a random fraction of the failing load. Within a Markov approximation, the breakdown…
In this paper we extend the Weibull power series (WPS) class of distributions and named this new class as extended Weibull power series (EWPS) class of distributions. The EWPS distributions are related to series and parallel systems with a…
A random fiber bundle model with a mixed Weibull distribution is studied under the Global Load Sharing (GLS) scheme. The mixed model consists of two sets of fibers. The threshold strength of one set of fibers are randomly chosen from a…
This paper presents two main results. The first result indicates that in materials with broadly distributed microscopic heterogeneities, the fracture strength distribution corresponding to the peak load of the material response does not…
We investigate the effect of the amount of disorder on the statistics of breaking bursts during the quasi-static fracture of heterogeneous materials. We consider a fiber bundle model where the strength of single fibers is sampled from a…
Possible distributions are discussed for intertrade durations and first-passage processes in financial markets. The view-point of renewal theory is assumed. In order to represent market data with relatively long durations, two types of…
We characterize the complex, heavy-tailed probability distribution functions (pdf) describing the response and its local extrema for structural systems subjected to random forcing that includes extreme events. Our approach is based on the…
We examine probability distribution for avalanche sizes observed in self-organized critical systems. While a power-law distribution with a cutoff because of finite system size is typical behavior, a systematic investigation reveals that it…
Reliability inference based on parametric distributions is an important problem in electrical and mechanical engineering. Most existing methods rely on approximations or bootstrap procedures, which may not perform satisfactorily when data…
Using a family of modified Weibull distributions, encompassing both sub-exponentials and super-exponentials, to parameterize the marginal distributions of asset returns and their multivariate generalizations with Gaussian copulas, we offer…
A theoretical scaling law for the size effect of the strength of brittle materials is presented. To some extend, it can be seen as an extension of the well known Weibull law. For that a correlated Random Fields is used to model the…