Related papers: Indirect identification of damage functions from d…
We consider the distribution of the sum and the maximum of a collection of independent exponentially distributed random variables. The focus is laid on the explicit form of the density functions (pdf) of non-i.i.d. sequences. Those are…
Two-term asymptotic formulae for the probability distribution functions for the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one of the…
In this paper, we propose that a tree-like network with damage can be modeled as the product of a fractional-order nominal plant and a fractional-order multiplicative disturbance, which is well structured and completely characterized by the…
We develop a general framework to analyze the distribution functions of wealth and income. Within this framework we study wealth distribution in a society by using a model which turns on two-party trading for poor people while for rich…
In this paper we use risk management techniques to evaluate the potential effects of those operational risks that affect the energy production of a wind farm. We concentrate our attention on three major risk factors: wind speed uncertainty,…
In this paper, we introduce the generalized Gompertz-power series class of distributions which is obtained by compounding generalized Gompertz and power series distributions. This compounding procedure follows same way that was previously…
Extreme environmental phenomena such as major precipitation events manifestly exhibit spatial dependence. Max-stable processes are a class of asymptotically-justified models that are capable of representing spatial dependence among extreme…
A closed set of \textit{exact} equations describing statistical theory of turbulent self-diffusion by multivariate-normal turbulent velocity field is derived. In doing so, we first suggest exact formulas for correlations…
In this note, we characterize the Gompertz distribution in terms of extreme value distributions and point out that it implicitly models the interplay of two antagonistic growth processes. In addition, we derive a closed form expressions for…
Statistical flood frequency analysis coupled with hydrograph scaling is commonly used to generate design floods to assess dam safety assessment. The safety assessments can be highly sensitive to the choice of the statistical flood frequency…
We point out that the functional form describing the frequency of sizes of events in complex systems (e.g. earthquakes, forest fires, bursts of neuronal activity) can be obtained from maximal likelihood inference, which, remarkably, only…
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…
We study extreme events of avalanche activities in finite-size two-dimensional self-organized critical (SOC) models, specifically the stochastic Manna model (SMM) and the Bak-Tang-Weisenfeld (BTW) sandpile model. Employing the approach of…
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
A continuous approximation for the results of [1] is obtained. In this approximation the energy distribution is represented in the form of the product of the Gibbs factor and superstatistics factor. The mutual weights of the factors are…
We consider the problem of predicting power outages in an electrical power grid due to hazards produced by convective storms. These storms produce extreme weather phenomena such as intense wind, tornadoes and lightning over a small area. In…
Our primary aim is to find an estimate of the expected shortfall in various situations: (1) Nonparametric situation, when the probability distribution of the incurred loss is unknown, only satisfying some general conditions. Then, following…
The last decade has seen numerous record-shattering heatwaves in all corners of the globe. In the aftermath of these devastating events, there is interest in identifying worst-case thresholds or upper bounds that quantify just how hot…
Understanding and predicting uncertain things are the central themes of scientific evolution. Human beings revolve around these fears of uncertainties concerning various aspects like a global pandemic, health, finances, to name but a few.…
It is demonstrated that World War II casualty data display statistical structure that would be expected from multifractal data. Given that the data displayed these properties, it is shown how the existence of power-law tails in the…