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Cramer-Rao efficiencies of best linear invariant estimators of parameters of the extreme-value distribution under type II censoring from above
Cramer-Rao efficiencies of best linear invariant estimators, using Weibull distribution in model for survival populations connected with life testing
The application of the statistical theory of extreme values to gust-load problems
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A new method of analyzing extreme-value data
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An Extreme-Value Approach to Anomaly Vulnerability Identification
The objective of this paper is to present a method for importance analysis in parametric probabilistic modeling where the result of interest is the identification of potential engineering vulnerabilities associated with postulated anomalies in system behavior. In the context of Accident Precursor Analysis (APA), under which this method has been developed, these vulnerabilities, designated as anomaly vulnerabilities, are conditions that produce high risk in the presence of anomalous system behavior. The method defines a parameter-specific Parameter Vulnerability Importance measure (PVI), which identifies anomaly risk-model parameter values that indicate the potential presence of anomaly vulnerabilities, and allows them to be prioritized for further investigation. This entails analyzing each uncertain risk-model parameter over its credible range of values to determine where it produces the maximum risk. A parameter that produces high system risk for a particular range of values suggests that the system is vulnerable to the modeled anomalous conditions, if indeed the true parameter value lies in that range. Thus, PVI analysis provides a means of identifying and prioritizing anomaly-related engineering issues that at the very least warrant improved understanding to reduce uncertainty, such that true vulnerabilities may be identified and proper corrective actions taken.
Extreme Value Snow Water Equivalent and Snowmelt for Infrastructure Design over the Contiguous United States
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Uncertainties in obtaining high reliability from stress-strength models
There has been a recent interest in determining high statistical reliability in risk assessment of aircraft components. The potential consequences are identified of incorrectly assuming a particular statistical distribution for stress or strength data used in obtaining the high reliability values. The computation of the reliability is defined as the probability of the strength being greater than the stress over the range of stress values. This method is often referred to as the stress-strength model. A sensitivity analysis was performed involving a comparison of reliability results in order to evaluate the effects of assuming specific statistical distributions. Both known population distributions, and those that differed slightly from the known, were considered. Results showed substantial differences in reliability estimates even for almost nondetectable differences in the assumed distributions. These differences represent a potential problem in using the stress-strength model for high reliability computations, since in practice it is impossible to ever know the exact (population) distribution. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability. An alternative reliability computation procedure is examined involving determination of a lower bound on the reliability values using extreme value distributions. This procedure reduces the possibility of obtaining nonconservative reliability estimates. Results indicated the method can provide conservative bounds when computing high reliability.
Statistic analysis of annual total ozone extremes for the period 1964-1988
Annual extremes of total column amount of ozone (in the period 1964-1988) from a network of 29 Dobson stations have been examined using the extreme value analysis. The extremes have been calculated as the highest deviation of daily mean total ozone from its long-term monthly mean, normalized by the monthly standard deviations. The extremes have been selected from the direct-Sun total ozone observations only. The extremes resulting from abrupt changes in ozone (day to day changes greater than 20 percent) have not been considered. The ordered extremes (maxima in ascending way, minima in descending way) have been fitted to one of three forms of the Fisher-Tippet extreme value distribution by the nonlinear least square method (Levenberg-Marguard method). We have found that the ordered extremes from a majority of Dobson stations lie close to Fisher-Tippet type III. The extreme value analysis of the composite annual extremes (combined from averages of the annual extremes selected at individual stations) has shown that the composite maxima are fitted by the Fisher-Tippet type III and the composite minima by the Fisher-Tippet type I. The difference between the Fisher-Tippet types of the composite extremes seems to be related to the ozone downward trend. Extreme value prognoses for the period 1964-2014 (derived from the data taken at: all analyzed stations, the North American, and the European stations) have revealed that the prognostic extremes are close to the largest annual extremes in the period 1964-1988 and there are only small regional differences in the prognoses.
Dataset for 'Ombadi et al. (2023). A warming-induced reduction in snow fraction amplifies rainfall extremes, Nature'
This package contains the main codes, sample input data and main result files to reproduce the analysis and results presented in the article: “Ombadi et al. (2023), A warming-induced reduction in snow fraction amplifies rainfall extremes, Nature”. The folder consists of the following: (1) “Raw data”: a folder that contains sample input data which is used in some of the codes for demonstration purposes. It also contains data that was not pre-processed such as Elevation data; (2) “Results”: this folder contains files of the main results presented in the paper including: “Annual-Max-Series”, “Change-rainfall-extremes”, “Change-snow-fraction”, “Warming levels_By scenario_model_year” and “Masks”. Description of these folders is detailed in the "Readme.rtf" file; (3) Python jupyter notebooks (Extract_Annual Max Series (AMS).ipynb, Elevation-dependent amplification of rainfall extremes.ipynb, Sensitivity_to_global_warming.ipynb) demonstrate the main steps of analysis. Further description of those notebooks is provided in the "Readme.rtf" file; (4) R code for extreme value analysis (Extreme_Value_Analysis.R). The sample and pre-processed dataset in "Raw data" is obtained from publicly available repositories of CMIP6 and ERA5 datasets; see Methods for more detail. This research was supported by Office of Science, Office of Biological and Environmental Research of the US Department of Energy under contract no. DE-AC02-05CH11231 for the CASCADE Scientific Focus (funded by the Regional and Global Model Analysis Program area within the Earth and Environmental Systems Modeling Program) and the iNAIADS Early Career Research Project (funded by the Environmental Systems Science program).
On the uncertainty of long-period return values of extreme daily precipitation
Methods for calculating return values of extreme precipitation and their uncertainty are compared using daily precipitation rates over the Western U.S. and Southwestern Canada from a large ensemble of climate model simulations. The roles of return-value estimation procedures and sample size in uncertainty are evaluated for various return periods. We compare two different generalized extreme value (GEV) parameter estimation techniques, namely L-moments and maximum likelihood (MLE), as well as empirical techniques. Even for very large datasets, confidence intervals calculated using GEV techniques are narrower than those calculated using empirical methods. Furthermore, the more efficient L-moments parameter estimation techniques result in narrower confidence intervals than MLE parameter estimation techniques at small sample sizes, but similar best estimates. It should be noted that we do not claim that either parameter fitting technique is better calibrated than the other to estimate long period return values. While a non-stationary MLE methodology is readily available to estimate GEV parameters, it is not for the L-moments method. Comparison of uncertainty quantification methods are found to yield significantly different estimates for small sample sizes but converge to similar results as sample size increases. Finally, practical recommendations about the length and size of climate model ensemble simulations and the choice of statistical methods to robustly estimate long period return values of extreme daily precipitation statistics and quantify their uncertainty.
Future Climate Projections for South Florida: Improving the Accuracy of Air Temperature and Precipitation Extremes With a Hybrid Statistical Bias Correction Technique
Projecting future climate variables is essential for comprehending the potential impacts on hydroclimatic hazards like floods and droughts. Evaluating these impacts is challenging due to the coarse spatial resolution of global climate models (GCMs); therefore, bias correction is widely used. Here, we applied two statistical methods—standard empirical quantile mapping (EQM) and a hybrid approach, EQM with linear correction (EQM-LIN)—to bias correct precipitation and air temperature simulated by nine GCMs. We used historical observations from 20 weather stations across South Florida to project future climate under three shared socioeconomic pathways (SSPs). Compared to the EQM, the hybrid EQM-LIN method improved R 2 of daily quantiles by up to 30% over the historical period and improved MAE up to 70% in months that contain most extreme values. Projected extreme precipitation at the weather stations showed that, compared to the EQM-LIN, the EQM method underestimates the high quantiles by up to 26% in SSP585. The projected changes in annual maximum precipitation from historical period (1985–2014) to near future (2040–2069) and far future (2070–2100) were between 2% and 16% across the study area. Projected future precipitation suggested a slight decrease during summer but an increase in fall. This, along with rising summer temperatures, suggested that South Florida can experience rapid oscillations from warmer summers and increased flooding in fall under future climate. Additionally, our comparative analyses with globally and nationally downscaled studies showed that such coarse scale studies do not represent the climatic extremes well, particularly for high quantile precipitation.
Evaluation of NASA's MERRA Precipitation Product in Reproducing the Observed Trend and Distribution of Extreme Precipitation Events in the United States
This study evaluates the performance of NASA's Modern-Era Retrospective Analysis for Research and Applications (MERRA) precipitation product in reproducing the trend and distribution of extreme precipitation events. Utilizing the extreme value theory, time-invariant and time-variant extreme value distributions are developed to model the trends and changes in the patterns of extreme precipitation events over the contiguous United States during 1979-2010. The Climate Prediction Center (CPC) U.S.Unified gridded observation data are used as the observational dataset. The CPC analysis shows that the eastern and western parts of the United States are experiencing positive and negative trends in annual maxima, respectively. The continental-scale patterns of change found in MERRA seem to reasonably mirror the observed patterns of change found in CPC. This is not previously expected, given the difficulty in constraining precipitation in reanalysis products. MERRA tends to overestimate the frequency at which the 99th percentile of precipitation is exceeded because this threshold tends to be lower in MERRA, making it easier to be exceeded. This feature is dominant during the summer months. MERRA tends to reproduce spatial patterns of the scale and location parameters of the generalized extreme value and generalized Pareto distributions. However, MERRA underestimates these parameters, particularly over the Gulf Coast states, leading to lower magnitudes in extreme precipitation events. Two issues in MERRA are identified: 1) MERRA shows a spurious negative trend in Nebraska and Kansas, which is most likely related to the changes in the satellite observing system over time that has apparently affected the water cycle in the central United States, and 2) the patterns of positive trend over the Gulf Coast states and along the East Coast seem to be correlated with the tropical cyclones in these regions. The analysis of the trends in the seasonal precipitation extremes indicates that the hurricane and winter seasons are contributing the most to these trend patterns in the southeastern United States. In addition, the increasing annual trend simulated by MERRA in the Gulf Coast region is due to an incorrect trend in winter precipitation extremes.
Winds aloft statistical analysis in support of day of launch Shuttle systems evaluation
In connection with the development of the Meteorological Interactive Data Display System (MIDDS) for utilization by the Launch Systems Evaluation Advisory Team (LSEAT), requirements have been established to expand the pre-launch analysis of winds aloft for the Space Shuttle. Statistical analyses developed for the system include: comparison of pre-launch wind component profiles to wind component extremes at each altitude calculated from launch site historical data; conditional probability ellipses for wind vectors at a future time given the wind vector at an initial time; comparison of observed extreme wind shear and associated wind speed with launch site historical data utilizing the bivariate extreme value (Gumbel) distribution; estimation of extremes of wind speed or wind shear at a future time given the extremes of either variable at an initial time, utilizing the conditional extreme value distribution; power spectrum analysis for tracking wind perturbation energy in sequential pre-launch Jimsphere wind profiles.
Isosurface Extraction in Time-Varying Fields Using a Temporal Hierarchical Index Tree
Many high-performance isosurface extraction algorithms have been proposed in the past several years as a result of intensive research efforts. When applying these algorithms to large-scale time-varying fields, the storage overhead incurred from storing the search index often becomes overwhelming. this paper proposes an algorithm for locating isosurface cells in time-varying fields. We devise a new data structure, called Temporal Hierarchical Index Tree, which utilizes the temporal coherence that exists in a time-varying field and adoptively coalesces the cells' extreme values over time; the resulting extreme values are then used to create the isosurface cell search index. For a typical time-varying scalar data set, not only does this temporal hierarchical index tree require much less storage space, but also the amount of I/O required to access the indices from the disk at different time steps is substantially reduced. We illustrate the utility and speed of our algorithm with data from several large-scale time-varying CID simulations. Our algorithm can achieve more than 80% of disk-space savings when compared with the existing techniques, while the isosurface extraction time is nearly optimal.
Quenching of single-particle strength inferred from nucleon-removal transfer reactions on 15 C
The difference in the proton and neutron separation energies (ΔS) of the weakly bound 15 C ground state is -19.86 MeV, an extreme value. Data from intermediate-energy heavy-ion induced (HI-induced) knockout reactions on nuclei spanning -20 ≲ ΔS ≲ +20 MeV, suggest that the degree to which single-particle strength is quenched, R s , has a negative correlation with ΔS, decreasing from unity around -20 MeV to around 0.2 at +20 MeV. For the 15 C ground state (R s = 0.96 (4) in HI-induced knockout), contrasting results have recently been obtained via the neutron-adding transfer reaction, which reveal a value of R s = 0.64 (15), similar to the value observed at modest and more extreme values of ΔS with reaction probes other than HI knockout. In order to explore the any potential differences between adding and removing processes in transfer reactions at extreme ΔS, single-neutron removal transfer reactions on 15 C were performed at 7.1 MeV/u in inverse kinematics. The removal of a valence neutron in 2s 1/2 orbit using both (p, d) and (d, t) reactions shows consistent quenching factors and agrees with those from the neutron-adding reaction. The present results, which can be compared with neutron knockout reaction, suggest that correlations, represented by the quenching factor, show limited dependence on neutron-proton asymmetry under the most extreme asymmetry conditions so far achieved in transfer reactions.
A Class of Sparse Johnson–Lindenstrauss Transforms and Analysis of their Extreme Singular Values
The Johnson–Lindenstrauss (JL) lemma is a powerful tool for dimensionality reduction in modern algorithm design. The lemma states that any set of high-dimensional points in a Euclidean space can be projected into lower dimensions while approximately preserving pairwise Euclidean distances. Random matrices satisfying this lemma are called JL transforms (JLTs). Inspired by existing $s$-hashing JLTs with exactly $s$ nonzero elements on each column, the present work introduces an ensemble of sparse matrices encompassing so-called $s$-hashing-like matrices whose expected number of nonzero elements on each column is $s$. The independence of the sub-Gaussian entries of these matrices and the knowledge of their exact distribution play an important role in their analyses. Using properties of independent sub-Gaussian random variables, these matrices are demonstrated to be JLTs, and their smallest nontrivial singular values and largest singular values are estimated nonasymptotically using a technique from geometric functional analysis. As the dimensions of the matrix grow to infinity, these singular values are proved to converge almost surely to fixed quantities (by using the universal Bai–Yin law) and in distribution to the Gaussian orthogonal ensemble Tracy–Widom law after proper rescalings. Understanding the behaviors of extreme singular values is important in general because they are often used to define a measure of stability of matrix algorithms. For example, JLTs were recently used in derivative-free optimization algorithmic frameworks to select random subspaces in which are constructed random models or poll directions to achieve scalability, and hence estimating their smallest singular value in particular helps determine the dimension of these subspaces.
On the modeling of scalar diffusion in isotropic turbulence
The objectives of the study were to establish the behavior of conditional scalar dissipation and diffusion at the extreme values of mass fraction and to derive and evaluate closure models for these terms using the scalar probability density function. The conditional scalar dissipation, its derivative with respect to mass fraction, and conditional scalar diffusion are all found to be zero at extreme values of mass fraction. A model for conditional scalar dissipation is derived which exhibits the correct behavior at the extreme values of scalar concentration.
Estimating maximum instantaneous distortion from inlet total pressure rms and PSD measurements
An inexpensive method is developed to determine the extreme values of instantaneous inlet distortion. This method also provides insight into the basic mechanics of unsteady inlet flow and the associated engine reaction. The analysis is based on fundamental fluid dynamics and statistical methods to provide an understanding of the turbulent inlet flow and quantitatively relate the rms level and power spectral density (PSD) function of the measured time variant total pressure fluctuations to the strength and size of the low pressure regions. The most probable extreme value of the instantaneous distortion is then synthesized from this information in conjunction with the steady state distortion. Results of the analysis show the extreme values to be dependent upon the steady state distortion, the measured turbulence rms level and PSD function, the time on point, and the engine response characteristics. Analytical projections of instantaneous distortion are presented and compared with data obtained by a conventional, highly time correlated, 40 probe instantaneous pressure measurement system.