Related papers: Estimating the maximum possible earthquake magnitu…
Statistical analysis of extremes can be used to predict the probability of future extreme events, such as large rainfalls or devastating windstorms. The quality of these forecasts can be measured through scoring rules. Locally scale…
Although researchers accumulated knowledge about seismogenesis and decades-long earthquake data, predicting imminent individual earthquakes at a specific time and location remains a long-standing enigma. This study hypothesizes that the…
Without rigorous attention to the completeness of earthquake catalogs, claims of new discoveries or forecasting skills cannot be deemed credible. Therefore, estimating the completeness magnitude (Mc) is a critical step. Among various…
We address several questions on the behavior of a numerical model recently introduced to study seismic phenomena, that includes relaxation in the plates as a key ingredient. We make an analysis of the scaling of the largest events with…
Extreme Value Theory plays an important role to provide approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the {generalised Pareto…
The empirical Bath's law is derived from the magnitude-difference statistical distribution of earthquake pairs. The pair distribution related to earthquake correlations is presented. The single-event distribution of dynamically correlated…
The \emph{Swift} Burst Alert Telescope (BAT), operating in the 15--150 keV energy band, struggles to detect the peak energy ($E_{\rm p}$) of gamma-ray bursts (GRBs), as most GRBs have $E_{\rm p}$ values typically distributed between 200-300…
The dragon-king earthquake hypothesis proposes that some very large to great earthquakes are not merely the extreme end of the frequency-magnitude Gutenberg-Richter distribution (FMD), but are generated by distinct physical mechanisms,…
Weather extremes are a major societal and economic hazard, claiming thousands of lives and causing billions of dollars in damage every year. Under climate change, their impact and intensity are expected to worsen significantly.…
We aim to analyze the behaviour of a finite-time stochastic system, whose model is not available, in the context of more rare and harmful outcomes. Standard estimators are not effective in making predictions about such outcomes due to their…
Typically, in the dynamical theory of extremal events, the function that gauges the intensity of a phenomenon is assumed to be convex and maximal, or singular, at a single, or at most a finite collection of points in phase--space. In this…
We consider the extremal shot noise defined by $$M(y)=\sup\{mh(y-x);(x,m)\in\Phi\},$$ where $\Phi$ is a Poisson point process on $\bbR^d\times (0,+\infty)$ with intensity $\lambda dxG(dm)$ and $h:\bbR^d\to [0,+\infty]$ is a measurable…
We introduce a consistent estimator of the extreme value index under random truncation based on a single sample fraction of top observations from truncated and truncation data. We establish the asymptotic normality of the proposed estimator…
Bayesian neural networks (BNN) are the probabilistic model that combines the strengths of both neural network (NN) and stochastic processes. As a result, BNN can combat overfitting and perform well in applications where data is limited.…
Extreme Value Theory (EVT) is one of the most commonly used approaches in finance for measuring the downside risk of investment portfolios, especially during financial crises. In this paper, we propose a novel approach based on EVT called…
In this work, we focus on some conditional extreme risk measures estimation for elliptical random vectors. In a previous paper, we proposed a methodology to approximate extreme quantiles, based on two extremal parameters. We thus propose…
A trigonometrically approximated maximum likelihood estimation for $\alpha$-stable laws is proposed. The estimator solves the approximated likelihood equation, which is obtained by projecting a true score function on the space spanned by…
We review highlights from string theory, black hole physics and doubly special relativity and some "thought" experiments which were suggested to probe the shortest distance and/or the maximum momentum at the Planck scale. The models which…
Although the fundamental probabilistic theory of extremes has been well developed, there are many practical considerations that must be addressed in application. The contribution of this thesis is four-fold. The first concerns the choice of…
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…