Slow closure of Earth's carbon cycle.

Carbon near the Earth's surface cycles between the production and consumption of organic carbon; the former sequesters carbon dioxide while the latter releases it. Microbes attempt to close the loop, but the longer organic matter survives, the slower microbial degradation becomes. This aging effect leaves observable quantitative signatures: Organic matter decays at rates that are inversely proportional to its age, while microbial populations and concentrations of organic carbon in ocean sediments decrease at distinct powers of age. Yet mechanisms that predict this collective organization remain unknown. Here, I show that these and other observations follow from the assumption that the decay of organic matter is limited by progressively rare extreme fluctuations in the energy available to microbes for decomposition. The theory successfully predicts not only observed scaling exponents but also a previously unobserved scaling regime that emerges when microbes subsist on the minimum energy flux required for survival. The resulting picture suggests that the carbon cycle's age-dependent dynamics are analogous to the slow approach to equilibrium in disordered systems. The impact of these slow dynamics is profound: They preclude complete oxidation of organic carbon in sediments, thereby freeing molecular oxygen to accumulate in the atmosphere.

Trends of extreme US weather events in the changing climate.

Trends in extreme 100-y events of temperature and rainfall amounts in the continental United States are estimated, to see effects of climate change. This is a nontrivial statistical problem because climate change effects have to be extracted from "noisy" weather data within a limited time range. We use nonparametric Bayesian methods to estimate the trends of extreme events that have occurred between 1979 and 2019, based on data for temperature and rainfall. We focus on 100-y events for each month in [Formula: see text] geographical areas looking at hourly temperature and 5-d cumulative rainfall. Distribution tail models are constructed using extreme value theory (EVT) and data on 33-y events. This work shows it is possible to aggregate data from spatial points in diverse climate zones for a given month and fit an EVT model with the same parameters. This surprising result means there are enough extreme event data to see the trends in the 41-y record for each calendar month. The yearly trends of the risk of a 100-y high-temperature event show an average 2.1-fold increase over the last 41 y of data across all months, with a 2.6-fold increase for the months of July through October. The risk of high rainfall extremes increases in December and January 1.4-fold, but declines by 22% for the spring and summer months.

Estimating cutoff values for diagnostic tests to achieve target specificity using extreme value theory.

BACKGROUND: Rapidly developing tests for emerging diseases is critical for early disease monitoring. In the early stages of an epidemic, when low prevalences are expected, high specificity tests are desired to avoid numerous false positives. Selecting a cutoff to classify positive and negative test results that has the desired operating characteristics, such as specificity, is challenging for new tests because of limited validation data with known disease status. While there is ample statistical literature on estimating quantiles of a distribution, there is limited evidence on estimating extreme quantiles from limited validation data and the resulting test characteristics in the disease testing context. METHODS: We propose using extreme value theory to select a cutoff with predetermined specificity by fitting a Pareto distribution to the upper tail of the negative controls. We compared this method to five previously proposed cutoff selection methods in a data analysis and simulation study. We analyzed COVID-19 enzyme linked immunosorbent assay antibody test results from long-term care facilities and skilled nursing staff in Colorado between May and December of 2020. RESULTS: We found the extreme value approach had minimal bias when targeting a specificity of 0.995. Using the empirical quantile of the negative controls performed well when targeting a specificity of 0.95. The higher target specificity is preferred for overall test accuracy when prevalence is low, whereas the lower target specificity is preferred when prevalence is higher and resulted in less variable prevalence estimation. DISCUSSION: While commonly used, the normal based methods showed considerable bias compared to the empirical and extreme value theory-based methods. CONCLUSIONS: When determining disease testing cutoffs from small training data samples, we recommend using the extreme value based-methods when targeting a high specificity and the empirical quantile when targeting a lower specificity.

Tail Risk Dynamics under Price-Limited Constraint: A Censored Autoregressive Conditional Fréchet Model.

This paper proposes a novel censored autoregressive conditional Fréchet (CAcF) model with a flexible evolution scheme for the time-varying parameters, which allows deciphering tail risk dynamics constrained by price limits from the viewpoints of different risk preferences. The proposed model can well accommodate many important empirical characteristics of financial data, such as heavy-tailedness, volatility clustering, extreme event clustering, and price limits. We then investigate tail risk dynamics via the CAcF model in the price-limited stock markets, taking entropic value at risk (EVaR) as a risk measurement. Our findings suggest that tail risk will be seriously underestimated in price-limited stock markets when the censored property of limit prices is ignored. Additionally, the evidence from the Chinese Taiwan stock market shows that widening price limits would lead to a decrease in the incidence of extreme events (hitting limit-down) but a significant increase in tail risk. Moreover, we find that investors with different risk preferences may make opposing decisions about an extreme event. In summary, the empirical results reveal the effectiveness of our model in interpreting and predicting time-varying tail behaviors in price-limited stock markets, providing a new tool for financial risk management.

Why is there an "oversupply" of human ovarian follicles?†.

Women are born with hundreds of thousands to over a million primordial ovarian follicles (PFs) in their ovarian reserve. However, only a few hundred PFs will ever ovulate and produce a mature egg. Why are hundreds of thousands of PFs endowed around the time of birth when far fewer follicles are required for ongoing ovarian endocrine function and only a few hundred will survive to ovulate? Recent experimental, bioinformatics, and mathematical analyses support the hypothesis that PF growth activation (PFGA) is inherently stochastic. In this paper, we propose that the oversupply of PFs at birth enables a simple stochastic PFGA mechanism to yield a steady supply of growing follicles that lasts for several decades. Assuming stochastic PFGA, we apply extreme value theory to histological PF count data to show that the supply of growing follicles is remarkably robust to a variety of perturbations and that the timing of ovarian function cessation (age of natural menopause) is surprisingly tightly controlled. Though stochasticity is often viewed as an obstacle in physiology and PF oversupply has been called "wasteful," this analysis suggests that stochastic PFGA and PF oversupply function together to ensure robust and reliable female reproductive aging.

Evidence that coronavirus superspreading is fat-tailed.

Superspreaders, infected individuals who result in an outsized number of secondary cases, are believed to underlie a significant fraction of total SARS-CoV-2 transmission. Here, we combine empirical observations of SARS-CoV and SARS-CoV-2 transmission and extreme value statistics to show that the distribution of secondary cases is consistent with being fat-tailed, implying that large superspreading events are extremal, yet probable, occurrences. We integrate these results with interaction-based network models of disease transmission and show that superspreading, when it is fat-tailed, leads to pronounced transmission by increasing dispersion. Our findings indicate that large superspreading events should be the targets of interventions that minimize tail exposure.

Risk modelling of ESG (environmental, social, and governance), healthcare, and financial sectors.

Climate change poses enormous ecological, socio-economic, health, and financial challenges. A novel extreme value theory is employed in this study to model the risk to environmental, social, and governance (ESG), healthcare, and financial sectors and assess their downside risk, extreme systemic risk, and extreme spillover risk. We use a rich set of global daily data of exchange-traded funds (ETFs) from 1 July 1999 to 30 June 2022 in the case of healthcare and financial sectors and from 1 July 2007 to 30 June 2022 in the case of ESG sector. We find that the financial sector is the riskiest when we consider the tail index, tail quantile, and tail expected shortfall. However, the ESG sector exhibits the highest tail risk in the extreme environment when we consider a shock in the form of an ETF drop of 25% or 50%. The ESG sector poses the highest extreme systemic risk when a shock comes from China. Finally, we find that ESG and healthcare sectors have lower extreme spillover risk (contagion risk) compared to the financial sector. Our study seeks to provide valuable insights for developing sustainable economic, business, and financial strategies. To achieve this, we conduct a comprehensive risk assessment of the ESG, healthcare, and financial sectors, employing an innovative approach to risk modelling in response to ecological challenges.

Bridging Extremes: The Invertible Bimodal Gumbel Distribution.

This paper introduces a novel three-parameter invertible bimodal Gumbel distribution, addressing the need for a versatile statistical tool capable of simultaneously modeling maximum and minimum extremes in various fields such as hydrology, meteorology, finance, and insurance. Unlike previous bimodal Gumbel distributions available in the literature, our proposed model features a simple closed-form cumulative distribution function, enhancing its computational attractiveness and applicability. This paper elucidates the behavior and advantages of the invertible bimodal Gumbel distribution through detailed mathematical formulations, graphical illustrations, and exploration of distributional characteristics. We illustrate using financial data to estimate Value at Risk (VaR) from our suggested model, considering maximum and minimum blocks simultaneously.

S-duct flow distortion with non-uniform inlet conditions.

Convoluted aero-engine intakes are often required to enable closer integration between engine and airframe. Although the majority of previous research focused on the distortion of S-duct intakes with undistorted inlet conditions, there is a need to investigate the impact of more challenging inlet conditions at which the intake duct is expected to operate. The impact of inlet vortices and total pressure profiles on the inherent unsteady flow distortion of an S-duct intake was assessed with stereo particle image velocimetry. Inlet vortices disrupted the characteristic flow switching mode but had a modest impact on the peak levels and unsteady fluctuations. Non-uniform inlet total pressure profiles increased the peak swirl intensity and its unsteadiness. The frequency of swirl angle fluctuations was sensitive to the azimuthal orientation of the non-uniform total pressure distribution. The modelling of peak distortion with the extreme value theory revealed that although for some inlet configurations the measured peak swirl intensity was similar, the growth rate of the peak values beyond the experimental observations was substantially different and it was related with the measured flow unsteadiness. This highlights the need of unsteady swirl distortion measurements and the use of statistical models to assess the time-invariant peak distortion levels. Overall, the work shows it is vital to include the effect of the inlet flow conditions as it substantially alters the characteristics of the complex intake flow distortion.

ESTIMATION FOR EXTREME CONDITIONAL QUANTILES OF FUNCTIONAL QUANTILE REGRESSION.

Quantile regression as an alternative to modeling the conditional mean function provides a comprehensive picture of the relationship between a response and covariates. It is particularly attractive in applications focused on the upper or lower conditional quantiles of the response. However, conventional quantile regression estimators are often unstable at the extreme tails, owing to data sparsity, especially for heavy-tailed distributions. Assuming that the functional predictor has a linear effect on the upper quantiles of the response, we develop a novel estimator for extreme conditional quantiles using a functional composite quantile regression based on a functional principal component analysis and an extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator under some regularity conditions, and compare it with other estimation methods using Monte Carlo simulations. Finally, we demonstrate the proposed method by empirically analyzing two real data sets.

Analysis of milk production and greenhouse gas emissions as a function of extreme variations in forage production among French dairy farms.

Many studies that investigate mitigation strategies of greenhouse-gas (GHG) emissions from farming systems often build farm typologies from average data from multiple farms. Results from farm typologies are useful for general purposes but fail to represent variability in farm characteristics due to management practices or climate conditions, particularly when considering consequences of extreme environmental events. This limitation raises the issue of better distinguishing, within datasets of farms, farms that have average characteristics from those that deviate from average trends, in order to improve assessment of how climate variability influences farm performance. We applied the statistical method called Extreme Value Theory (EVT) to identify dairy farms that produced "extreme" amounts of forage. Applying EVT to a dataset of dairy farms from Normandy, Lorraine and Nord-Pas-de-Calais (France) identified subsamples of 10-30% of dairy farms with the smallest or largest amounts of grass from pastures or maize silage in each region. Characteristics of farms with extreme amounts of each forage often differed among regions due to the influence of geography and climate. Farms with the largest amounts of grass or the smallest amounts of maize silage had a variety of cow breeds in Normandy and Lorraine but had only Holstein cows in Nord-Pas-de-Calais. Conversely, most farms with the smallest amounts of grass or the largest amounts of maize silage had Holstein cows, regardless of region. The region also influenced whether farms were oriented more toward producing milk with higher fat and protein contents (Normandy and Lorraine) or toward producing larger amounts of milk (Nord-Pas-de-Calais). As the amount of a given forage changed from smallest to largest, a significant increase or decrease in the amount of milk produced usually changed GHG and enteric methane (CH4) emissions per farm in the same direction as the amount of milk produced. For instance, an extreme increase in the amount of grass fed on farms (1314 vs. 5093 kg/livestock unit/year, respectively) in Normandy was associated with decreased mean milk production (8236 vs. 5834 l/cow/year, respectively) and GHG (7117 vs. 5587 kg CO2 eq./farm/year) and enteric CH4 (3870 vs. 3296 kg CO2 eq./farm/year, respectively) emissions.

Extreme quantile estimation for partial functional linear regression models with heavy-tailed distributions.

In this article, we propose a novel estimator of extreme conditional quantiles in partial functional linear regression models with heavy-tailed distributions. The conventional quantile regression estimators are often unstable at the extreme tails due to data sparsity, especially for heavy-tailed distributions. We first estimate the slope function and the partially linear coefficient using a functional quantile regression based on functional principal component analysis, which is a robust alternative to the ordinary least squares regression. The extreme conditional quantiles are then estimated by using a new extrapolation technique from extreme value theory. We establish the asymptotic normality of the proposed estimator and illustrate its finite sample performance by simulation studies and an empirical analysis of diffusion tensor imaging data from a cognitive disorder study.

Dans cet article, un nouvel estimateur de quantiles conditionnels extrêmes est élaboré dans le cadre de modèles de régression linéaire fonctionnelle partielle avec des distributions à queues lourdes. Il est bien connu que la rareté des observations dans les ailes extrêmes de distributions à queues lourdes rend souvent les estimateurs de régression quantile usuels instables. Pour parer à la non robustesse des moindres carrés classiques, les auteurs ont commencé par estimer la fonction de pente et le coefficient partiellement linéaire d'une régression quantile en ayant recours à une approche basée sur l'analyse en composantes principales fonctionnelles. Ensuite, ils ont estimé les quantiles conditionnels extrêmes à l'aide d'une nouvelle technique d'extrapolation issue de la théorie des valeurs extrêmes. En plus d'établir la normalité asymptotique de l'estimateur proposé, les auteurs illustrent ses bonnes performances à distance finie par le biais d'une étude de simulation et une mise en oeuvre pratique sur les données d'imagerie de diffusion par tenseurs provenant d'une étude portant sur des troubles cognitifs.

Baseline Methods for the Parameter Estimation of the Generalized Pareto Distribution.

In the parameter estimation of limit extreme value distributions, most employed methods only use some of the available data. Using the peaks-over-threshold method for Generalized Pareto Distribution (GPD), only the observations above a certain threshold are considered; therefore, a big amount of information is wasted. The aim of this work is to make the most of the information provided by the observations in order to improve the accuracy of Bayesian parameter estimation. We present two new Bayesian methods to estimate the parameters of the GPD, taking into account the whole data set from the baseline distribution and the existing relations between the baseline and the limit GPD parameters in order to define highly informative priors. We make a comparison between the Bayesian Metropolis-Hastings algorithm with data over the threshold and the new methods when the baseline distribution is a stable distribution, whose properties assure we can reduce the problem to study standard distributions and also allow us to propose new estimators for the parameters of the tail distribution. Specifically, three cases of stable distributions were considered: Normal, Lévy and Cauchy distributions, as main examples of the different behaviors of the tails of a distribution. Nevertheless, the methods would be applicable to many other baseline distributions through finding relations between baseline and GPD parameters via studies of simulations. To illustrate this situation, we study the application of the methods with real data of air pollution in Badajoz (Spain), whose baseline distribution fits a Gamma, and show that the baseline methods improve estimates compared to the Bayesian Metropolis-Hastings algorithm.

Copula-based measures of asymmetry between the lower and upper tail probabilities.

We propose a copula-based measure of asymmetry between the lower and upper tail probabilities of bivariate distributions. The proposed measure has a simple form and possesses some desirable properties as a measure of asymmetry. The limit of the proposed measure as the index goes to the boundary of its domain can be expressed in a simple form under certain conditions on copulas. A sample analogue of the proposed measure for a sample from a copula is presented and its weak convergence to a Gaussian process is shown. Another sample analogue of the presented measure, which is based on a sample from a distribution on R 2 , is given. Simple methods for interval and region estimation are presented. A simulation study is carried out to investigate the performance of the proposed sample analogues and methods for interval estimation. As an example, the presented measure is applied to daily returns of S&P500 and Nikkei225. A trivariate extension of the proposed measure and its sample analogue are briefly discussed. Supplementary Information: The online version contains supplementary material available at 10.1007/s00362-022-01297-w.

The impacts of digital finance development on household income, consumption, and financial asset holding: an extreme value analysis of China's microdata.

This paper examines the roles of digital finance development in household income, consumption, and financial asset holding from an extreme value theory perspective. Three types of extreme pairs (Min to Min, Max to Max, and Max to Min) are constructed, corresponding to the three aspects of the economic welfare of digital finance: fairness, efficiency, and their trade-off. Using panel data from the Peking University Digital Financial Inclusion Index of China (PKU-DFIIC) and China Family Panel Studies (CFPS) over time span 2014-2018, this paper models the block maxima and minima of variables by fitting them with generalized extreme value (GEV) distribution. The binary expansion testing (BET) is used to detect the nonlinear dependence between digital finance and household economic variables. The tail quotient correlation coefficient (TQCC) is used to quantify the tail dependencies. The results show that: (1) digital finance has significant fairness effects in reducing poverty, increasing consumption, and promoting financial asset holding; (2) digital finance shows effects of promoting incentives and efficiency in household income and financial asset holding, but this effect is relatively limited in household consumption; (3) digital finance generally increases efficiency without harming fairness in terms of all cases of household income and consumption, and most of the cases regarding household financial asset holding; (4) the positive spatial externality of digital finance exists for all household economic variables; and, for pairs regarding household income and consumption, the wider the scope, the greater the spatial spillover effect. The result of this paper implies many novel policy implications.

Return Period Evaluation of the Largest Possible Earthquake Magnitudes in Mainland China Based on Extreme Value Theory.

The largest possible earthquake magnitude based on geographical characteristics for a selected return period is required in earthquake engineering, disaster management, and insurance. Ground-based observations combined with statistical analyses may offer new insights into earthquake prediction. In this study, to investigate the seismic characteristics of different geographical regions in detail, clustering was used to provide earthquake zoning for Mainland China based on the geographical features of earthquake events. In combination with geospatial methods, statistical extreme value models and the right-truncated Gutenberg-Richter model were used to analyze the earthquake magnitudes of Mainland China under both clustering and non-clustering. The results demonstrate that the right-truncated peaks-over-threshold model is the relatively optimal statistical model compared with classical extreme value theory models, the estimated return level of which is very close to that of the geographical-based right-truncated Gutenberg-Richter model. Such statistical models can provide a quantitative analysis of the probability of future earthquake risks in China, and geographical information can be integrated to locate the earthquake risk accurately.

Carbon neutrality: The role of banks in optimal environmental management strategies.

This study explores the ecological ambitions of banks by studying the coincidence of economic realities with environmental management strategies. We address this question by studying the environmental performance of US banks and its impact on their tail risk as US is not committed to carbon neutrality in COP 21. We proxy economic reality with tail risk of banks and employ a novel extreme value theory to measure this. We use Asset4 ESG data for environmental performance score and test our hypothesis with a sample of 256 US banks. The results indicate that the US banks are ecologically ambitious and their environmental strategies are likely to reduce their tail risk. This provides evidence that better environmental strategies do coincide with the economic realities. We test the consistency of our results by using alternate proxies for tail risk and find our results robust. Our results are also not driven by endogeneity concerns. Finally, our additional results show that the nature of relationship differs with corporate governance levels, CSR committee existence, institutional ownership presence and crisis period.

Extreme Value Theory for Hurwitz Complex Continued Fractions.

The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and an extreme value law. The results are based on cusp estimates of the invariant measure about which information is still limited. In the process, we obtained several results concerning the extremes of nearest integer continued fractions as well.

On Max-Semistable Laws and Extremes for Dynamical Systems.

Suppose (f,X,µ) is a measure preserving dynamical system and ϕ:X→R a measurable observable. Let Xi=ϕ∘fi-1 denote the time series of observations on the system, and consider the maxima process Mn:=max{X1,…,Xn}. Under linear scaling of Mn, its asymptotic statistics are usually captured by a three-parameter generalised extreme value distribution. This assumes certain regularity conditions on the measure density and the observable. We explore an alternative parametric distribution that can be used to model the extreme behaviour when the observables (or measure density) lack certain regular variation assumptions. The relevant distribution we study arises naturally as the limit for max-semistable processes. For piecewise uniformly expanding dynamical systems, we show that a max-semistable limit holds for the (linear) scaled maxima process.

Extreme Value Theory in Application to Delivery Delays.

This paper uses the Extreme Value Theory (EVT) to model the rare events that appear as delivery delays in road transport. Transport delivery delays occur stochastically. Therefore, modeling such events should be done using appropriate tools due to the economic consequences of these extreme events. Additionally, we provide the estimates of the extremal index and the return level with the confidence interval to describe the clustering behavior of rare events in deliveries. The Generalized Extreme Value Distribution (GEV) parameters are estimated using the maximum likelihood method and the penalized maximum likelihood method for better small-sample properties. The findings demonstrate the advantages of EVT-based prediction and its readiness for application.