Extreme Value Statistics Research Articles

Ytterbium-doped fiber laser as a source of coexisting narrow-band thermal light and optical rogue waves: Experimental demonstration

In this paper, we show that a continuous-wave ytterbium-doped fiber laser implemented in the conventional configuration of a Fabry-Perot cavity with two fiber Bragg gratings as selective reflectors and a moderate output power (tens of watts) generates two groups of photons, each of which is characterized by its own statistics. The statistics of the first group are described by the M−fold degenerate Bose-Einstein distribution, where M is the number of independent states of spontaneous emission, which, in turn, depends on the laser linewidth and the radiofrequency band of the recording equipment. This kind of light is classified as narrow-band thermal light. The second group of photons is described by the extreme-value exponential statistics with a probability of encountering extremely large photon events much greater than expected from the Bose-Einstein distribution, which is classified as optical rogue waves. At a low laser power, the first group of photons strongly dominates over the second. As the laser power increases, the fraction of photons of the second group increases monotonically; above a certain threshold, the fraction of this group increases, reaching tens of percent of the total number of laser photons.

Breaking the chains: Extreme value statistics and localization in random spin chains

Breaking the chains: Extreme value statistics and localization in random spin chains

Machine learning-assisted extreme value statistics of anomalies in AlSi10Mg manufactured by L-PBF for robust fatigue strength predictions

Traditional Extreme Value Statistics (EVS) applied to block maxima sampled anomalies of components produced by Laser-Powder Bed Fusion may produce important inaccuracies in the estimated characteristic defects. In fact, the typical presence of multiple defect types may significantly affect the fitted maxima distributions obtained from different sampling volumes. In this work, we show how the limitations of traditional EVS can be overcome by applying supervised machine learning (ML) algorithms to classify the defects before estimating the maxima distributions for each defect type. The ML-assisted EVS provided maxima distributions unaffected by the different sampling volumes. The obtained maxima distribution lead to robust estimates of exceedance curves and finally, by employing the Shiozawa curve, to robust fatigue strength predictions.

Extremal statistics for a resetting Brownian motion before its first-passage time.

We study the extreme value statistics of a one-dimensional resetting Brownian motion (RBM) till its first passage through the origin starting from the position x_{0} (>0). By deriving the exit probability of RBM in an interval [0,M] from the origin, we obtain the distribution P_{r}(M|x_{0}) of the maximum displacement M and thus gives the expected value 〈M〉 of M as functions of the resetting rate r and x_{0}. We find that 〈M〉 decreases monotonically as r increases, and tends to 2x_{0} as r→∞. In the opposite limit, 〈M〉 diverges logarithmically as r→0. Moreover, we derive the propagator of RBM in the Laplace domain in the presence of both absorbing ends, and then leads to the joint distribution P_{r}(M,t_{m}|x_{0}) of M and the time t_{m} at which this maximum is achieved in the Laplace domain by using a path decomposition technique, from which the expected value 〈t_{m}〉 of t_{m} is obtained explicitly. Interestingly, 〈t_{m}〉 shows a nonmonotonic dependence on r, and attains its minimum at an optimal r^{*}≈2.71691D/x_{0}^{2}, where D is the diffusion coefficient. Finally, we perform extensive simulations to validate our theoretical results.

Kernel estimator of extreme value index (EVI) and high quantiles for heavy-tailed distributions under dependence serials using the Box-Cox transformation

The Box-Cox transformation is used to render the data more conducive to statistical analysis. Its application to extreme values statistics improves the convergence rate of certain classical tail index estimators and reduces bias in the context of independent and identically distributed (i.i.d) random variables. In this paper, we explore a bias reduction estimator for the extreme value index under $\beta$-mixing serial dependence. Our approach is based on kernel estimation of the extreme value index and the Box-Cox transformation methodology. Under specific regular conditions, we establish the asymptotic normality of the proposed estimator and deduce an asymptotically unbiased estimator for high quantiles. Through a simulation study, we delineate the performance of our proposals, comparing them to alternative estimators recently introduced in the literature. We further illustrate these theoretical results by applying them to real wind speed data.

Predicting Failure Distributions of SRAM Arrays by Using Extreme Value Statistic, Bit Cell Simulation, and Machine Learning

We present a successful methodology for accurately predicting failure distributions of SRAM arrays based on simulation results of a single bit cell. This was achieved by using extreme value statistic and a data-centric approach of supervised machine learning. The purpose of such predictions is to enable assessments of the trade-off between optimizing power, performance, and area (PPA) and safeguarding reliability in an early phase of development.

QUANTIFYING THE BELGIAN COAST’S RESILIENCE AGAINST SEA LEVEL RISE (USING XBEACH and SWASH MODELLING)

To maintain however a safe and climate resilient coast, it is utterly important to bridge the knowledge gap between its current safety level and its safety level under sea level rise. That’s why this year’s safety assessment includes also 3 mean sea level rise scenario’s: +0.3, +0.8 and +1.5m. It allows us to quantify the strength of the sea defense under changing hydraulic conditions and, possibly, identify its tipping point. Applying joint probability analysis and extreme value statistics on long time series of field data (monitored on the Belgian continental shelf) results in combinations of wind, water level and significant wave height having a specific (higher) return period. These combinations are then transformed from offshore to nearshore (just outside the surf zone) using SWAN. The Belgian coast is subdivided in alongshore coastal areas having similar median grain sizes. For every area, a 2DH XBeach model is set up, making use of a digital elevation model (DEM) of the present situation (February 2022).

Statistical modelling of dependence between net demands and deficits in two area power systems

Power system resource adequacy risks is dominated by the extremes of the relevant distributions or processes: the upper tail of demand and the lower tail of available generation. Because of this, relevant data in the historic record are sparse. Moreover, for interconnected systems, the degree of statistical dependence in these extremes between systems can also have a sizeable impact on the level of risk in each system. This paper uses results from statistical extreme value theory (EVT) to fit smoothed joint distributions for the values of (demand minus available renewables) and of surplus/deficit dependence in a two-area system, using data from the Irish and Great Britain power system for examples.As well as the statistical smoothing mitigating the consequences of limited volumes of data, the concept of asymptotic dependence provides a useful explanation of the strength of dependence. There is strong evidence that the deficits in the GB and Ireland systems are asymptotically independent, whereas there is evidence for asymptotic dependence in the distributions of (demand minus available wind capacity). This is consistent with the intuition that, when independent distributions of conventional capacity are convoluted with those of demand and wind, the dependence is weakened. The consequent use of a Gaussian copula to describe the dependence of deficits provides a convenient means of carrying out sensitivity analysis to the strength of relationship.

An extreme value statistics model of heterogeneous ice nucleation for quantifying the stability of supercooled aqueous systems.

The propensity of water to remain in a metastable liquid state at temperatures below its equilibrium melting point holds significant potential for cryopreserving biological material such as tissues and organs. The benefits conferred are a direct result of progressively reducing metabolic expenditure due to colder temperatures while simultaneously avoiding the irreversible damage caused by the crystallization of ice. Unfortunately, the freezing of water in bulk systems of clinical relevance is dominated by random heterogeneous nucleation initiated by uncharacterized trace impurities, and the marked unpredictability of this behavior has prevented the implementation of supercooling outside of controlled laboratory settings and in volumes larger than a few milliliters. Here, we develop a statistical model that jointly captures both the inherent stochastic nature of nucleation using conventional Poisson statistics as well as the random variability of heterogeneous nucleation catalysis through bivariate extreme value statistics. Individually, these two classes of models cannot account for both the time-dependent nature of nucleation and the sample-to-sample variability associated with heterogeneous catalysis, and traditional extreme value models have only considered variations of the characteristic nucleation temperature. We conduct a series of constant cooling rate and isothermal nucleation experiments with physiological saline solutions and leverage the statistical model to evaluate the natural variability of kinetic and thermodynamic nucleation parameters. By quantifying freezing probability as a function of temperature, supercooled duration, and system volume while accounting for nucleation site variability, this study also provides a basis for the rational design of stable supercooled biopreservation protocols.

Extreme value statistics and Arcsine laws of Brownian motion in the presence of a permeable barrier

The Arcsine laws of Brownian motion are a collection of results describing three different statistical quantities of one-dimensional Brownian motion: the time at which the process reaches its maximum position, the total time the process spends in the positive half-space and the time at which the process crosses the origin for the last time. Remarkably the cumulative probabilities of these three observables all follow the same distribution, the Arcsine distribution. But in real systems, space is often heterogeneous, and these laws are likely to hold no longer. In this paper we explore such a scenario and study how the presence of a spatial heterogeneity alters these Arcsine laws. Specifically we consider the case of a thin permeable barrier, which is often employed to represent diffusion impeding heterogeneities in physical and biological systems such as multilayer electrodes, electrical gap junctions, cell membranes and fragmentation in the landscape for dispersing animals. Using the Feynman–Kac formalism and path decomposition techniques we are able to find the exact time-dependence of the probability distribution of the three statistical quantities of interest. We show that a permeable barrier has a large impact on these distributions at short times, but this impact is less influential as time becomes long. In particular, the presence of a barrier means that the three distributions are no longer identical with symmetry about their means being broken. We also study a closely related statistical quantity, namely, the distribution of the maximum displacement of a Brownian particle and show that it deviates significantly from the usual half-Gaussian form.

AMICO galaxy clusters in KiDS-DR3: Constraints on ΛCDM from extreme value statistics

ABSTRACT We constrain the ΛCDM cosmological parameter σ8 by applying the extreme value statistics for galaxy cluster mass on the AMICO KiDS-DR3 catalogue. We sample the posterior distribution of the parameters by considering the likelihood of observing the largest cluster mass value in a sample of Nobs = 3644 clusters with intrinsic richness λ* > 20 in the redshift range z ∈ [0.10, 0.60]. We obtain $\sigma _{8}=0.90_{-0.18}^{+0.20}$, consistent within 1σ with the measurements obtained by the Planck collaboration and with previous results from cluster cosmology exploiting AMICO KiDS-DR3. The constraints could improve by applying this method to forthcoming missions, such as Euclid and LSST, which are expected to deliver thousands of distant and massive clusters.

Pitting Corrosion of Mild Steel in Long-Term Contact with Particulate Media in Seawater

Steel infrastructure in contact with particulate media is at risk of failure due to pitting corrosion. For reliability analysis, it is important to understand the progression of pit depth with time and the associated extreme value statistics. An analysis was conducted on an extensive dataset of pit depth observations, made on mild steel coupons buried in different particulate media and immersed in natural Pacific Ocean seawater. It showed that the trends for the deepest pits with time were consistent with the bimodal model, and that pitting was deepest under seawater and increased with particle size when under particulate media. Gumbel plots of the data showed that the deepest pits plotted as a straight line, indicating a good fit. The plots also showed small, regular deviations from this straight line, and these permitted interpretations for pit depths developing in incremental steps. These step sizes were largest for surfaces under seawater and increased with increasing particle size under particulate media. These findings allowed for new conceptual models for the process of pit depth growth under rust and particulate media. They also allow for new insights into metastable pitting for steels. Opportunities for further research are also presented.

Seismicity Based Maximum Magnitude Estimation of Subduction Earthquakes in Peru

In seismic design, intensity parameters that represent seismic demand are commonly used. A probabilistic seismic hazard assessment is an accurate way of assessing seismic demand, based on a set of parameters that represent the seismicity of a region. However, because some regions lack sufficient information, the selection of these parameters can be controversial. In Peru, selecting a maximum earthquake magnitude (Mmax) for regional seismic hazard assessments has proven to be a challenging task due to the limited available information concerning of large-magnitude events. This study evaluated the Mmax for subduction earthquakes using scaling relationships, empirical evidence, and the extreme value statistics (Kijko and Bayesian) approach. The seismic catalog was updated to February 2022 and divided into 19 subduction seismic sources (5 interface and 14 intraslab). The results showed that the obtained Mmax are within the range of Mw 8.7–9.0 for the interface and Mw 7.6–8.1 for the intraslab sources, which unlike the Mmax values established in previous regional seismic hazard assessments, are more consistent with the historical and instrumental seismicity and rupture models.

The unprecedented spatial extent and intensity of the 2021 summer extreme heatwave event over the Western North American regions

A record-breaking heatwave event occurred in western North America in the summer of 2021. Previous studies on a similar event's uniqueness and return period are typically estimated based on extreme value analysis and statistics of selected stations or area-mean temperature data. The extreme statistics results are no longer valid if moved to another location. Further, the detailed evolution of spatial extent and intensity through its duration is not quantified and compared to other historical heatwave events to claim its rarity and severity. By applying an event detection and tracking algorithm to heatwaves, we first construct an archive for all the events over the region since 1979 based on daily maximum temperature data from reanalysis. It documented the daily mean temperature anomalies, affected areas, and durations of all individual heatwave events. It is, therefore, possible to objectively compare and rank the magnitudes of all historical heatwave events by examining the total integrated effects from the intensity, impact region, and duration. With the global mean warming background increase of about 0.4 °C from 1979 to 2000 to 2000–2021, we found that the mean integrated magnitude and size of the top 100 heatwave events increased significantly by 155 ± 88%. The dominant relative contributions to this integrated severity measure increase are +78 ± 39% from the mean affected area, followed by +54 ± 21% from duration and +7 ± 4% from the intensity. With the above analyzed general historical increasing trend of heatwave event metrics, the severity of the 2021 summer heatwave over the region was due to a combination of its record-breaking event-mean spatial coverages (2090383 km2), highest normalized daily maximum temperature anomalies and long duration (11 days, in the top 4% of all heatwave events). This integrated severity measure of the event was more than double of any other historical heatwave event and about 17 times larger than the mean severity of all heatwave events over the region.

Effect of Ruhrstahl Heraeus Refining Time on Inclusions and Rolling Contact Fatigue Life of a High‐Carbon Chromium Bearing Steel

According to the variation in the average composition, the average size, the number density, and the area fraction of large‐size inclusions during Ruhrstahl Heraeus (RH) refining process, large‐size inclusions in the high‐carbon chromium‐bearing steel reach the lowest level when the vacuum cycle time is 25 min. When the soft blowing time reaches over 25 min, the number density and area fraction of large‐size inclusions increase. The rolling contact fatigue (RCF) life of the forged steel samples is measured using a thrust RCF tester, indicating that the fatigue life of no. 1 steel (vacuum cycle 40 min, soft blowing 20 min) is 12% higher than that of no. 2 steel (vacuum cycle 20 min, soft blowing 40 min). Based on the estimation of the characteristic size of inclusions in the forged steel by the statistics of extreme values (SEV) method, it is concluded that when the characteristic size and the chemical composition of inclusions in steels are similar, the RCF life is increased by 12% when the number density of large‐size inclusions decreases from 0.63 to 0.44 mm−2.

A mixed distribution approach for low-flow frequency analysis – Part 2: Comparative assessment of a mixed probability vs. copula-based dependence framework

Abstract. In climates with a warm and a cold season, low flows are generated by different processes, which violates the homogeneity assumption of extreme value statistics. In this second part of a two-part series, we extend the mixed probability estimator of the companion paper (Laaha, 2023) to deal with dependency of seasonal events. We formulate a copula-based estimator for seasonal minima series and examine it in a hydrological context. The estimator is a valid generalization of the annual probability estimator and provides a consistent framework for estimating return periods of summer, winter, and annual events. Using archetypal examples we show that differences in the mixed estimator are always observed in the upper part of the distribution, which is less relevant for low-flow frequency analysis. The differences decrease as the return period increases so that both models coincide for the severest events. In a quantitative evaluation, we test the performance of the copula estimator on a pan-European data set. We find a large gain of both mixed distribution approaches over the annual estimator, making these approaches highly relevant for Europe as a whole. We then examine the relative performance gain of the mixed copula versus the mixed distribution approach in more detail. The analysis shows that the differences in the 100-year event are actually minimal. However, the differences in 2-year events are considerable in some of the catchments, with a relative deviation of −15 % to −25 % in the most affected regions. This points to a prediction bias of the mixed probability estimator that can be corrected using the copula approach. Using multiple regression models, we show that the performance gain can be well explained on hydrological grounds, with weak seasonality leading to a high potential for corrections and strong seasonal correlation reinforcing the need to take this potential into account. Accordingly, the greatest differences can be observed in mid-mountain regions in cold and temperate climates, where rivers have a strongly mixed low-flow regime. This finding is of particular relevance for event mapping, where regional severity can be misinterpreted when the seasonal correlation is neglected. We conclude that the two mixed probability estimators are quite similar, and both are conceptually more adequate than the annual minima approach for mixed summer and winter low-flow regimes. In regions with strong seasonal correlation the mixed copula estimator appears most appropriate and should be preferred over the mixed distribution approach.

Extreme value statistics of edge currents in Markov jump processes and their use for entropy production estimation

The infimum of an integrated current is its extreme value against the direction of its average flow. Using martingale theory, we show that the infima of integrated edge currents in time-homogeneous Markov jump processes are geometrically distributed, with a mean value determined by the effective affinity measured by a marginal observer that only sees the integrated edge current. In addition, we show that a marginal observer can estimate a fraction of the average entropy production rate in the underlying nonequilibrium process from the extreme value statistics in the integrated edge current. The estimated average rate of dissipation obtained in this way equals the above mentioned effective affinity times the average edge current. Moreover, we show that estimates of dissipation based on extreme value statistics can be significantly more accurate than those based on thermodynamic uncertainty ratios, as well as those based on a naive estimator obtained by neglecting nonMarkovian correlations in the Kullback-Leibler divergence of the trajectories of the integrated edge current.

Gaidai reliability method for long-term coronavirus modelling.

Novel coronavirus disease has been recently a concern for worldwide public health. To determine epidemic rate probability at any time in any region of interest, one needs efficient bio-system reliability approach, particularly suitable for multi-regional environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of novel coronavirus infection rate. Traditional statistical methods dealing with temporal observations of multi-regional processes do not have the multi-dimensionality advantage, that suggested methodology offers, namely dealing efficiently with multiple regions at the same time and accounting for cross-correlations between different regional observations. Modern multi-dimensional novel statistical method was directly applied to raw clinical data, able to deal with territorial mapping. Novel reliability method based on statistical extreme value theory has been suggested to deal with challenging epidemic forecast. Authors used MATLAB optimization software. This paper described a novel bio-system reliability approach, particularly suitable for multi-country environmental and health systems, observed over a sufficient period of time, resulting in a reliable long-term forecast of extreme novel coronavirus death rate probability. Namely, accurate maximum recorded patient numbers are predicted for the years to come for the analyzed provinces. The suggested method performed well by supplying not only an estimate but 95% confidence interval as well. Note that suggested methodology is not limited to any specific epidemics or any specific terrain, namely its truly general. The only assumption and limitation is bio-system stationarity, alternatively trend analysis should be performed first. The suggested methodology can be used in various public health applications, based on their clinical survey data.

Predicting the Number of Fatalities in Extreme Civil Aviation Accidents

This study estimates the probability of extreme fatalities from civil airplane accidents in the United States since the early 1980s. To this end, extreme civil airplane accidents were modeled using extreme value statistics, allowing for changes in the distribution due to other factors. The analysis revealed that an extreme aircraft accident causes 18 to 20 fatalities every two years with costs between 111.6 and 124 million U.S. dollars (USD); whereas accidents with (at least) between 70 and 100 fatalities will occur every 20 years, costing between 424 and 620 million USD. The findings also indicate that higher volumes of air traffic increase the return levels of severe aviation accidents, whereas higher ticket prices reduce the likelihood of these. The findings emphasize the serious consequences of airplane accidents with respect to the number of fatalities but also how these depend on market conditions.

Extreme Value Statistics for Evolving Random Networks

Our objective is to survey recent results concerning the evolution of random networks and related extreme value statistics, which are a subject of interest due to numerous applications. Our survey concerns the statistical methodology but not the structure of random networks. We focus on the problems arising in evolving networks mainly due to the heavy-tailed nature of node indices. Tail and extremal indices of the node influence characteristics like in-degrees, out-degrees, PageRanks, and Max-linear models arising in the evolving random networks are discussed. Related topics like preferential and clustering attachments, community detection, stationarity and dependence of graphs, information spreading, finding the most influential leading nodes and communities, and related methods are surveyed. This survey tries to propose possible solutions to unsolved problems, like testing the stationarity and dependence of random graphs using known results obtained for random sequences. We provide a discussion of unsolved or insufficiently developed problems like the distribution of triangle and circle counts in evolving networks, or the clustering attachment and the local dependence of the modularity, the impact of node or edge deletion at each step of evolution on extreme value statistics, among many others. Considering existing techniques of community detection, we pay attention to such related topics as coloring graphs and anomaly detection by machine learning algorithms based on extreme value theory. In order to understand how one can compute tail and extremal indices on random graphs, we provide a structured and comprehensive review of their estimators obtained for random sequences. Methods to calculate the PageRank and PageRank vector are shortly presented. This survey aims to provide a better understanding of the directions in which the study of random networks has been done and how extreme value analysis developed for random sequences can be applied to random networks.