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Microgrids are resources that can be used to restore critical loads after a natural disaster, enhancing resilience of a distribution network. To deal with the stochastic nature of intermittent energy resources, such as wind turbines (WTs)…
In this paper I have studied the fiber bundle model with a fraction {\alpha} of infinitely strong fibers. Inclusion of such unbreakable fraction has been proven to affect the failure process in early studies, especially around a critical…
The distribution of return intervals of extreme events is studied in time series characterized by finite-term correlations with non-exponential decay. Precisely, it has been analyzed the statistics of the return intervals of extreme values…
The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of…
Power law distributed fluctuations are known to accompany \emph{terminal} failure in disordered brittle solids. The associated intermittent scale-free behavior is of interest from the fundamental point of view as it emerges universally from…
We show analytically that the answer to the question, "The longer it has been since the last earthquake, the longer the expected time till the next ?" depends crucially on the statistics of the fluctuations in the interval times between…
We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0\leq \alpha \leq 1 of the bundle is strong and it is…
In various applications of heavy-tail modelling, the assumed Pareto behavior is tempered ultimately in the range of the largest data. In insurance applications, claim payments are influenced by claim management and claims may for instance…
Predicting the occurrence of tail events is of great importance in financial risk management. By employing the method of peak-over-threshold (POT) to identify the financial extremes, we perform a recurrence interval analysis (RIA) on these…
The critical behaviour of a Random Fiber Bundle Model with mixed uniform distribution of threshold strengths and global load sharing rule is studied with a special emphasis on the nature of distribution of avalanches for different…
Convective available potential energy (CAPE) is of strong interest in climate modeling because of its role in both severe weather and in model construction. Extreme levels of CAPE ($>$ 2000 J/kg) are associated with high-impact weather…
Physical systems characterized by stick-slip dynamics often display avalanches. Regardless of the diversity of their microscopic structure, these systems are governed by a power-law distribution of avalanche size and duration. Here we focus…
In statistical process control Weibull distribution can be used to model the time between events or failures (TBE) in a process with increasing decreasing or constant failure rates. Specifically it helps in monitoring processes where the…
A key building block in the design of ultra-reliable communication systems is a wireless channel model that captures the statistics of rare events occurring due to significant fading. In this paper, we propose a novel methodology based on…
A new statistical approach has been developed to analyze Resistive Random Access Memory (RRAM) variability. The stochastic nature of the physical processes behind the operation of resistive memories makes variability one of the key issues…
We study the critical behavior of the component sizes for the configuration model when the tail of the degree distribution of a randomly chosen vertex is a regularly-varying function with exponent $\tau-1$, where $\tau\in (3,4)$. The…
We study random fiber bundle model (RFBM) with different threshold strength distributions and load sharing rules. A mixed RFBM within global load sharing scheme is introduced which consists of weak and strong fibers with uniform…
The aim of this article is to determine a new six-parameter Beta Weibull distribution and its various associated functions, namely the cumulative distribution, survival, probability density and hazard functions. Next, we determine the…
In this paper, we investigate how much of the numerical artefacts introduced by finite system size and choice of boundary conditions can be removed by finite size scaling, for strongly-correlated systems with quasi-long-range order.…
The random fiber bundle (RFB) model, with the strength of the fibers distributed uniformly within a finite interval, is studied under the assumption of global load sharing among all unbroken fibers of the bundle. At any fixed value of the…