Related papers: Finite-Size Effects on Return Interval Distributio…
The Weibull function is widely used to describe skew distributions observed in nature. However, the origin of this ubiquity is not always obvious to explain. In the present paper, we consider the well-known Galton-Watson branching process…
In nature, granular materials fail in abrupt avalanches, earthquakes, and other hazardous events, and also creep over time. Proposed failure mechanisms for these systems are broadly framed as friction-limited. However, mechanical…
We analyse the balls in bins process with feedback with primary focus on the power law feedback function $f(\omega)=\eta \omega^{\gamma}\,$, $\eta>0\,$ $\gamma \geq0\,$. Using the recursive solution to the master equation we find for power…
Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting…
This paper introduces a new generalization of the power generalized Weibull distribution called the generalized power generalized Weibull distribution. This distribution can also be considered as a generalization of Weibull distribution.…
Copula modeling consists in finding a probabilistic distribution, called copula, whereby its coupling with the marginal distributions of a set of random variables produces their joint distribution. The present work aims to use this…
Extreme values and the tail behavior of probability distributions are essential for quantifying and mitigating risk in complex systems of all kinds. In multivariate settings, accounting for correlations is crucial. Although extreme value…
This paper introduces a novel deep learning method, called DeepWKB, for estimating the invariant distribution of randomly perturbed systems via its Wentzel-Kramers-Brillouin (WKB) approximation $u_\epsilon(x) = Q(\epsilon)^{-1}…
Robustness and cascading failures in interdependent systems has been an active research field in the past decade. However, most existing works use percolation-based models where only the largest component of each network remains functional…
This paper introduces a new two-parameter distribution, referred to as the Shiha distribution, which provides a flexible model for skewed lifetime data with either heavy or light tails. The proposed distribution is applicable to various…
We study the effect on the distribution of return periods of rare events of the presence in a time series of finite-term correlations with non-exponential decay. Precisely, we analyze the auto-correlation function and the statistics of the…
We study finite size effects for the gap of the quasiparticle excitation spectrum in the weakly interacting regime one-dimensional Hubbard model with on-site attraction. Two type of corrections to the result of the thermodynamic limit are…
Heavy-tailed distributions are widely used in robust mixture modelling due to possessing thick tails. As a computationally tractable subclass of the stable distributions, sub-Gaussian $\alpha$-stable distribution received much interest in…
We address the statistics of continuous weak linear measurement on a few-state quantum system that is subject to a conditioned quantum evolution. For a conditioned evolution, both the initial and final states of the system are fixed: the…
For measuring tail risk with scarce extreme events, extreme value analysis is often invoked as the statistical tool to extrapolate to the tail of a distribution. The presence of large datasets benefits tail risk analysis by providing more…
Turbulence locally created in laminar pipe flows shows sudden decay or splitting after a stochastic waiting time. In laboratory experiments, the mean waiting time was observed to increase double-exponentially as the Reynolds number (Re)…
We study the distributions of the resilience of power flow models against transmission line failures via a so-called backup capacity. We consider three ensembles of random networks and in addition, the topology of the British transmission…
Weak convergence of maxima of dependent sequences of identically distributed continuous random variables is studied under normalizing sequences arising as subsequences of the normalizing sequences from an associated iid sequence. This…
Some authors have recently argued that a finite-size scaling law for the text-length dependence of word-frequency distributions cannot be conceptually valid. Here we give solid quantitative evidence for the validity of such scaling law,…
We present a probabilistic framework for brittle fracture that builds upon Weibull statistics and strain gradient plasticity. The constitutive response is given by the mechanism-based strain gradient plasticity theory, aiming to accurately…