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In this paper, we study via simulation the performance of irregular repetition slotted ALOHA under multi-packet detection and different patterns of the load process. On the one hand, we model the arrival process with a version of the M/G/∞ process able to exhibit a correlation structure decaying slowly in time. Given the independence among frames in frame-synchronous coded-slotted ALOHA (CSA), this variation should only take effect on frame-asynchronous CSA. On the other hand, we vary the marginal distribution of the arrival process using discrete versions of the Lognormal and Pareto distributions, with the objective of investigating the influence of the right tail. In this case, both techniques should be affected by the change, albeit to a different degree. Our results confirm these hypotheses and show that these factors must be taken into account when designing and analyzing these systems. In frameless operations, both the shape of the packet arrivals tail distribution and the existence of short-range and long-range correlations strongly impact the packet loss ratio and the average delay. Nevertheless, these effects emerge only weakly in the case of frame-aligned operations, because this enforces the system to introduce a delay in the newly arrived packets (until the beginning of the next frame), and implies that the backlog of accumulated packets is the key quantity for calculating the performance. [ABSTRACT FROM AUTHOR]

Context. The constant growth in the volume of information, the increase in the speed of information flows in digital communication networks, as before, makes the task of assessing the service stability for traffic flows an urgent one. A simple solution to ensure high service stability is to build a network of sufficient capacity for any traffic that will be thrown at it. To solve the problems of analyzing telecommunication systems, it is necessary to have appropriate models and engineering methods that allow to assess the service stability and predict the characteristics of their operation based on measurement data. In these conditions, the development of new methods for analyzing the traffic of multiservice networks that provide simplicity of calculations and their acceptable accuracy becomes especially relevant. Objective. The purpose of this paper is to study the traffic and service stability for users. Method. We propose a hybrid method for detecting anomalies in multiservice network traffic that uses algorithms without identification, adaptation and Mamdani fuzzy inference. The peculiarity of multiservice traffic as an object for assessing the existence of anomalies is the presence of stochastic processes in it subject to different distribution laws. For the experimental evaluation of the proposed method and algorithms, we have chosen the Poisson and Pareto distribution laws that define the limiting cases of traffic regularity. The method allows for monitoring and managing faults in a multiservice network in order to determine the causes of their occurrence. The following requirements are imposed on the developed algorithms for detecting anomalies in the traffic on multiservice networks: functioning in real or near real time; maintaining a given service stability; simplicity of implementation. The algorithms belong to the class of adaptive hybrid algorithms for identifying traffic parameters. They are used for both stationary and nonstationary traffic. Traffic is modeled as stochastic processes. Each belongs to the corresponding class, which is determined by the law of distribution of stochastic processes. Results. Experimental evaluation of the proposed method and algorithms has shown that they allow us to estimate the trends of these stochastic processes in real time, with high accuracy and while maintaining the service stability. Conclusions. The application of the developed method of troubleshooting management in a multiservice environment helps to improve the service stability by timely detecting problems, reducing the time of their elimination and reducing downtime, which, in turn, affects the increase in service reliability. [ABSTRACT FROM AUTHOR]

Accurate estimation of annual exceedance probabilities (AEPs) of extreme rainfalls through rainfall frequency analysis is a critical step in engineering design for flood mitigation and disaster response. Here we show how the estimation of rainfall frequency curves can be improved by fitting a four‐parameter Kappa distribution to a peaks‐over‐threshold (POT) series. To fit the Kappa distribution to POT data we present a two‐step fitting approach based on maximum likelihood estimation which separately models storm intensity and the arrival frequency. First, a Generalized Pareto distribution (GPA) describing storm intensity is fitted, followed by a Binomial distribution for storm arrivals. We compare the performance of this two‐step Kappa approach to an analogous two‐step Generalized Extreme Value (GEV) approach and to Kappa and GEV distributions fitted to annual maxima series (AMS), using both synthetic and real‐world data representative of Australian climatic conditions. The experiments show that leveraging additional information from the POT series in the two‐step Kappa approach dramatically improves quantile estimation and reduces uncertainty compared to fitting either the GEV or the Kappa distributions to AMS, particularly for rare quantiles. When skew–kurtosis properties of extreme rainfalls are well represented by the Kappa but not the GEV, the two‐step Kappa approach yields unbiased quantiles under extrapolation, while the use of GEV can lead to highly biased estimates. From these results, we believe the two‐step Kappa approach is suitable for both at‐site and regional rainfall frequency analyses as it can accommodate distributions ranging from GPA to GEV without encountering over‐fitting problems generally associated with four‐parameter distributions. Plain Language Summary: Estimating the annual probability of extreme storms is a key step in estimating the risk of flooding for infrastructure design. The most common approach for estimating rainfall probabilities involves fitting a model to a series of data of the single largest storm in each year (called an annual maxima series [AMS]). This approach does not use all the information in the rainfall record and generally limits hydrologists to adopting three‐parameter models. These models are often not flexible enough to represent the behavior of extreme rainfalls. A more information‐rich alternative is to fit a probability model to all storm events larger than a specified threshold (called a peaks‐over‐threshold [POT] series). Here, we assess the advantages of using the additional information contained in the POT series to fit a four‐parameter model (the Kappa distribution) to capture the behavior of extreme rainfalls. We introduce a two‐step fitting approach that separates the parameters relevant to storm intensity from those governing storm arrival frequency. Our results show that the Kappa model performs as well or better than a three‐parameter model fitted to either POT or AMS in a range of scenarios and conclude that the proposed approach is a practical alternative to traditional methods. Key Points: Novel, two‐step approach to fit the four‐parameter Kappa distribution to peaks‐over‐threshold data is presentedStorm intensity (Generalized Pareto distribution) and the storm arrival frequency (Binomial distribution) are modeled separatelyTwo‐step approach performs as well or better than a Generalized Extreme Value distribution fitted to annual maxima in a range of modeling experiments [ABSTRACT FROM AUTHOR]

The Port-Bouët Bay shoreline is threatened by extreme sea level (ESL) events, which result from the combination of storm tide, wave run-up, and sea level rise (SLR). This study provides comprehensive scenarios of current and future ESLs at the local scale along the bay to understand the evolution of the phenomenon and promote local adaptation. The methodological steps involve first reconstructing historical storm tide and wave run-up data using a hydrodynamic model (D-flow FM) and the empirical model of Stockdon et al. Second, the Generalized Pareto Distribution (GPD) model fitted to the Peaks-Over-Thresholds (POT) method is applied to the data to calculate extreme return levels. Third, we combine the extreme storm tide and wave run-up using the joint probability method to obtain the current ESLs. Finally, the current ESLs are integrated with recent SLR projections to provide future ESL estimates. The results show that the current ESLs are relatively high, with 100-year return levels of 4.37 m ± 0.51, 4.97 m ± 0.57, and 4.48 m ± 0.5 at Vridi, Petit-Bassam, and Sogefiha respectively. By end-century, under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios, the future SLR is expected to increase the current ESLs by 0.49 m, 0.62 m, and 0.84 m, respectively. This could lead to a more frequent occurrence of the current 100-year return period, happening once every 2 years by 2100, especially under SSP5-8.5. The developed SLR scenarios can be used to assess the potential coastal flood risk in the study area for sustainable and effective coastal management and planning. [ABSTRACT FROM AUTHOR]

We introduce a smooth-transition generalized Pareto (GP) regression model to study the time-varying dependence structure between extreme losses and a set of economic factors. In this model, the distribution of the loss size is approximated by a GP distribution, and its parameters are related to explanatory variables through regression functions, which themselves depend on a time-varying predictor of structural changes. We use this approach to study the dynamics in the monthly severity distribution of operational losses at a major European bank. Using the VIX as a transition variable, our analysis reveals that when the uncertainty is high, a high number of losses in a recent past are indicative of less extreme losses in the future, consistent with a self-inhibition hypothesis. On the contrary, in times of low uncertainty, only the growth rate of the economy seems to be a relevant predictor of the likelihood of extreme losses. [ABSTRACT FROM AUTHOR]

All the available information and uncertainties should be taken into account in a model to give correct answer to a stated problem and evaluate the performance of a structure. This study deals with the impact of parameter estimation uncertainty in extreme wind speeds on the assessed reliability index using frequentist approach. The peak-over-threshold approach with an automated threshold selection method is applied and bootstrapping is used to determine the 95% confidence interval of the estimated reliability index. Based on the results practical recommendations, i.e., a framework of this procedure are derived on how to handle peak-over-threshold in extreme wind speed models for the application of the proposed performance-based wind engineering design. [ABSTRACT FROM AUTHOR]

This article elaborates on a peaks over threshold (POT) model with earthquake samples based on the Pareto distribution. We analyze the earthquakes using the POT model in the eastern Bayan Har block. The result shows that the area experiences an earthquake above [Formula: see text] 7.5 every 30 years and a large earthquake above [Formula: see text] 7.8 every 100 years. The average magnitude of earthquakes above [Formula: see text] 5.2 that occur in the area every 5 years is [Formula: see text] 7.1 or greater. The upper limit of the theoretical magnitude predicted by the model is [Formula: see text] 8.7. Therefore, the risk of geological hazards is high in this area.

The formalism of geometrothermodynamics has been developed to describe the properties of thermodynamic systems in terms of concepts of differential geometry. On the other hand, in econophysics, it is argued that under certain conditions the behavior of economic systems can be described by using the laws of classical thermodynamics. These two results are used in this work to propose a geometric description of economic systems. We obtain as a result that most systems can be described by two different geometries corresponding to the Boltzmann–Gibbs and Pareto distributions, which represent two different population groups that are usually present in most economic systems. The geometrothermodynamic analysis shows that no phase transitions are present in the Boltzmann–Gibbs sector, whereas the Pareto sector is characterized by a strong thermodynamic interaction that leads to the appearance of a rich phase transition structure. We argue that those phase transitions could be interpreted as financial crises. [ABSTRACT FROM AUTHOR]

Context. Many massive galaxies launch jets from the accretion disk of their central black hole, but only 03 instances are known in which the associated outflows form giant radio galaxies (GRGs, or giants): luminous structures of megaparsec extent that consist of atomic nuclei, relativistic electrons, and magnetic fields. Large samples are imperative to understanding the enigmatic growth of giants, and recent systematic searches in homogeneous surveys constitute a promising development. For the first time, it is possible to perform meaningful precision statistics with GRG lengths, but a framework to do so is missing. Aims. We measured the intrinsic GRG length distribution by combining a novel statistical framework with a LOFAR Two-metre Sky Survey (LoTSS) sample of freshly discovered giants. In turn, this allowed us to answer an array of questions on giants. For example, we can now assess how rare a 5 Mpc giant is compared with one of 1 Mpc, and how much larger - given a projected length - the corresponding intrinsic length is expected to be. Notably, we can now also infer the GRG number density in the Local Universe. Methods. We assumed the intrinsic GRG length distribution to be Paretian (i.e. of power-law form) with tail index, and predicted the observed distribution by modelling projection and selection effects. To infer, we also systematically searched the LoTSS for hitherto unknown giants and compiled the largest catalogue of giants to date. Results. We show that if intrinsic GRG lengths are Pareto distributed with index, then projected GRG lengths are also Pareto distributed with index. Selection effects induce curvature in the observed projected GRG length distribution: angular length selection flattens it towards the lower end, while surface brightness selection steepens it towards the higher end. We explicitly derived a GRG's posterior over intrinsic lengths given its projected length, laying bare the dependence. We also discovered 2060 giants within LoTSS DR2 pipeline products; our sample more than doubles the known population. Spectacular discoveries include the largest, second-largest, and fourth-largest GRG known (lp = 5:1 Mpc, lp = 5:0 Mpc, and lp = 4:8 Mpc), the largest GRG known hosted by a spiral galaxy (lp = 2:5 Mpc), and the largest secure GRG known beyond redshift 1 (lp = 3:9 Mpc). We increase the number of known giants whose angular length exceeds that of the Moon from 10 to 23; among the discoveries is the angularly largest known radio galaxy in the Northern Sky, which is also the angularly largest known GRG (= 2). Combining theory and data, we determined that intrinsic GRG lengths are well described by a Pareto distribution, and measured the index = 3:5:5. This implies that, given its projected length, a GRG's intrinsic length is expected to be just 15% larger. Finally, we determined the comoving number density of giants in the Local Universe to be nGRG = 5 100 Mpc 3. Conclusions. We developed a practical mathematical framework that elucidates the statistics of giant radio galaxy lengths. Through a LoTSS search, we also discovered 2060 new giants. By combining both advances, we determined that intrinsic GRG lengths are well described by a Pareto distribution with index = 3:5 = 0:5, and that giants are truly rare in a cosmological sense: most clusters and filaments of the CosmicWeb are not currently home to a giant. Thus, our work yields new observational constraints for analytical models and simulations featuring radio galaxy growth. [ABSTRACT FROM AUTHOR]

In this paper, the two-parameter Pareto lifetime distribution is considered with vague shape and scale parameters, where parameters are set as generalized intuitionistic fuzzy numbers. A new L-R type intuitionistic fuzzy number is introduced, and cuts of the new fuzzy set are provided. The generalized intuitionistic fuzzy reliability characteristics such as reliability, conditional reliability, hazard rate and mean time to failure functions are defined, along with the special case of the two-parameter Pareto generalized intuitionistic fuzzy reliability analysis. Furthermore, the series and parallel system reliability are evaluated by the generalized intuitionistic fuzzy sets. Finally, for certain cases of the fuzzy shape and scale parameters and cut set values, the generalized intuitionistic fuzzy reliability characteristics are provided and compared through several illustrative plots. [ABSTRACT FROM AUTHOR]

Point prediction of future record values from a sequence of independent and identically distributed Pareto and Lomax random variables is addressed. The focus is on likelihood-based prediction techniques; in particular, the maximum likelihood as well as the maximum observed likelihood prediction principles are invoked to derive predictors. Pitman closeness criterion is used for comparing the prediction procedures, which are applied to real data. Moreover, one-sided prediction intervals are also addressed. [ABSTRACT FROM AUTHOR]

The Devylder–Goovaerts conjecture is probably the oldest conjecture in actuarial mathematics and has received a lot of attention in recent years. It claims that ruin with equalized claim amounts is always less likely than in the classical model. Investigating the validity of this conjecture is important both from a theoretical aspect and a practical point of view, as it suggests that one always underestimates the risk of insolvency by replacing claim amounts with the average claim amount a posteriori. We first state a simplified version of the conjecture in the discrete-time risk model when one equalizes aggregate claim amounts and prove that it holds. We then use properties of the Pareto distribution in risk theory and other ideas to target candidate counterexamples and provide several counterexamples to the original Devylder–Goovaerts conjecture. [ABSTRACT FROM AUTHOR]

In randomized clinical trials, methods of pairwise comparisons such as the 'Net Benefit' or the 'win ratio' have recently gained much attention when interests lies in assessing the effect of a treatment as compared to a standard of care. Among other advantages, these methods are usually praised for delivering a treatment measure that can easily handle multiple outcomes of different nature, while keeping a meaningful interpretation for patients and clinicians. For time‐to‐event outcomes, a recent suggestion emerged in the literature for estimating these treatment measures by providing a natural handling of censored outcomes. However, this estimation procedure may lead to biased estimates when tails of survival functions cannot be reliably estimated using Kaplan–Meier estimators. The problem then extrapolates to the other outcomes incorporated in the pairwise comparison construction. In this work, we suggest to extend the procedure by the consideration of a hybrid survival function estimator that relies on an extreme value tail model through the Generalized Pareto distribution. We provide an estimator of treatment effect measures that notably improves on bias and remains easily apprehended for practical implementation. This is illustrated in an extensive simulation study as well as in an actual trial of a new cancer immunotherapy. [ABSTRACT FROM AUTHOR]

Recently, there has been an increase in the occurrence of extreme high-temperature events across the China–Pakistan Economic Corridor (CPEC). Regional spatiotemporal identification and evaluation of extreme high temperatures are essential for accurate forecasting of future climate changes. When such events generate a meteorological hazard, it is important to understand their temporal and spatial features, return period, and identification criteria. Accurately identifying extreme events can help assess risk and predict their spatial–temporal variation. While past studies have focused on individual sites, extreme heat events generally manifest as spatially and temporally continuous regional events. In this study, we propose an objective identification technique based on gridded data and spatiotemporal continuity to reveal the spatiotemporal characteristics of intensity, frequency, and duration events of extreme heat events in the CPEC from May to October between 1961 and 2015. Furthermore, we estimate the return period of extreme heat in the study region using the generalized Pareto distribution (GPD). Our findings indicate that the historical extreme temperature events (intensity, frequency, and duration) in the CPEC have significantly increased. Areas with a high incidence of extreme heat events are concentrated in eastern Balochistan, northern Sindh, and southeastern Punjab. These findings suggest that disaster prevention and mitigation plans should be targeted towards areas with a high frequency of extreme heat events in the CPEC, allowing policy makers to better prepare for and respond to future events. [ABSTRACT FROM AUTHOR]

Estimation based on probability-weighted moments is a well-established method and an excellent alternative to the classic method of moments or the maximum likelihood method, especially for small sample sizes. In this research, we developed a new class of estimators for the parameters of the Pareto type I distribution. A generalization of the probability-weighted moments approach is the foundation for this new class of estimators. It has the advantage of being valid in the entire parameter space of the Pareto distribution. We established the asymptotic normality of the new estimators and applied them to simulated and real datasets in order to illustrate their finite sample behavior. The results of comparisons with the most used estimation methods were also analyzed. [ABSTRACT FROM AUTHOR]

The tail process Y = (Y i) i ∈ Z d of a stationary regularly varying random field X = (X i) i ∈ Z d represents the asymptotic local distribution of X as seen from its typical exceedance over a threshold u as u → ∞ . Motivated by the standard Palm theory, we show that every tail process satisfies an invariance property called exceedance-stationarity and that this property, together with the spectral decomposition of the tail process, characterizes the class of all tail processes. We then restrict to the case when Y i → 0 as | i | → ∞ and establish a couple of Palm-like dualities between the tail process and the so-called anchored tail process which, under suitable conditions, represents the asymptotic distribution of a typical cluster of extremes of X . The main message is that the distribution of the tail process is biased towards clusters with more exceedances. Finally, we use these results to determine the distribution of a typical cluster of extremes for moving average processes with random coefficients and heavy-tailed innovations. [ABSTRACT FROM AUTHOR]

Point prediction of future record values based on sequences of previous lower or upper records is considered by means of the method of maximum product of spacings, where the underlying distribution is assumed to be a power function distribution and a Pareto distribution, respectively. Moreover, exact and approximate prediction intervals are discussed and compared with regard to their expected lengths and their percentages of coverage. The focus is on deriving explicit expressions in the point and interval prediction procedures. Predictions and forecasts are of interest, e.g., in sports analytics, which is gaining more and more attention in several sports disciplines. Previous works on forecasting athletic records have mainly been based on extreme value theory. The presented statistical prediction methods are exemplarily applied to data from various disciplines of athletics as well as to data from American football based on fantasy football points according to the points per reception scoring scheme. The results are discussed along with basic assumptions and the choice of underlying distributions. [ABSTRACT FROM AUTHOR]

To measure uncertainties within anomaly detection and distinguish sensor faults from anomalous events, a multi-index probabilistic anomaly detection approach is proposed for large span bridges based on Bayesian estimation and evidential reasoning. To avoid false detection raised by signal spikes, an energy index is first defined and extracted from pre-processed measurements, including missing data recovery and thermal response separation. Then, a probabilistic index, namely, certainty degree, is derived from probability density functions of detection triggers – extreme values predicted by using Bayesian estimation of the generalized Pareto distribution. To distinguish sensor faults from anomalous scenarios, evidential reasoning is applied to incorporate multiple certainty degrees into a joint one under the assumption that the probability of multi-sensor failing simultaneously is extremely low. Specifically, a large joint certainty degree indicates a high occurrence probability of anomalous scenarios, while a small one together with a large individual certainty degree depicts a high probability of sensor faults. Finally, the effectiveness of the proposed anomaly detection method is validated through structural health monitoring data from the Nanjing Dashengguan Yangtze River Bridge. Measurements from four sensors, that is, three cable forces and one deflection, are selected to detect anomalies based on their high pair-wise correlations. Two case studies are presented, namely, sensor fault detection and snow disaster detection. The sensor fault is detected through a certainty degree of almost 100% for the individual index and a joint certainty degree of nearly 0. The snowstorm is detected by a joint certainty degree of 36.82%. [ABSTRACT FROM AUTHOR]

We consider estimation and prediction of future records based on observed records from the new Pareto type distribution proposed recently by Bourguignon et al. (2016), ¡°M. Bourguignon, H. Saulo, R. N. Fernandez, A new Pareto-type distribution with applications in reliability and income data, Physica A, 457 (2016), 166-175¡±. We first obtain the maximum likelihood and Bayesian estimators of the model parameters. We then derive several point predictors for a future record on the basis of the first n observed records. Two real data sets on precipitation and Covid 19 are analysed and a Monte Carlo simulation study has been performed to evaluate the statistical performance of point predictors presented in this paper. [ABSTRACT FROM AUTHOR]

Abstract—A mathematical model is developed to study via simulation the impact of burst-mode packet-switched traffic propagating through an optical link constituted of single mode fiber (SMF) and dispersion compensating fiber (DCF). A modified Two-stage EDFA containing two identical doped fibers separated with an inverted trapezoidal optical filter (ITOF) is used. A simple dynamic model of EDFA including signal, pump and both forward and backward ASE powers propagation. A nonlinear Schrödinger equation is used to describe the propagation of eight WDM channels under the influence of linear and nonlinear effects. Channels are modeled as ON-OFF asynchronous transfer mode (ATM) source, statically independent, randomly generated with truncated Pareto distribution. We are able to perceive the variance of power level by which a WDM can be pushed into unsuitable power and optical signal-to-noise ratio (OSNR) swings involving a distorted signal shape in the presence of linear and nonlinear effects. The results show distortions that occur as a result of the presence of the gain cross saturation and the linear and nonlinear effects on packet-switched burst-mode traffic in the WDM link; The investigation results, presented as histograms, estimate the power, gain and OSNR at the link output. These distortions reveal a high-power level during the OFF periods when it was supposed to transmit no power through it. [ABSTRACT FROM AUTHOR]

While it is well known that water availability controls vegetation growth and soil microbial activity, how aridity affects ecosystem carbon patterns is not completely understood. Toward a more quantitative assessment of terrestrial carbon stocks, here we apply dimensional analysis and scaling to the global joint distribution of terrestrial carbon stock, obtained from international survey data and harmonized global maps. The results show a remarkable self‐similar behavior of the global carbon stock with dryness index, whereby the key statistics (e.g., mean, quantiles, and standard deviation) of carbon stock tend to scale with the hydroclimatic regime (i.e., aridity) via a universal exponent. Such a scaling reflects the strong coupling between the hydrological cycle and biogeochemical process and enables robust predictions of carbon stocks as a function of aridity only. When normalized by its averages in the corresponding hydroclimatic regime, the carbon stock distributions collapse onto a single double Pareto lognormal distribution, often used in economics to describe income. The presence of this distribution in completely different physical contexts, such as biogeochemistry and economics, hints at generating mechanisms that transcend the details of the specific stock being considered. Plain Language Summary: Water is essential to plant growth and soil microbial communities, which control the amount of total carbon stored over the land in the form of biomass and soil organic carbon. Yet, the global carbon patterns are still not very clear, especially with regard to the statistics in different ecosystems. Here by analyzing international survey data and harmonized global maps of carbon stocks we find a new relationship between terrestrial carbon storage and the aridity index, a quantity commonly used to quantify the local soil water availability. The carbon storage distributions for the same aridity index have similar shapes with relatively large probabilities of both extremely high or low carbon stocks across all terrestrial ecosystems. Such features allow us to gain information on future carbon stocks and inform climate mitigation planning. Key Points: Key statistics of terrestrial carbon stocks scale with the hydroclimatic regime via a universal exponentThe carbon stock distributions in each hydroclimatic regime, when normalized by their averages, collapse onto a single curveSelf‐similar scaling predicts carbon loss of 7.3 Pg C for 1% increase of global aridity [ABSTRACT FROM AUTHOR]

Probability-based distributions might be able to explain risk exposure well. Usually, one number, or at the very least, a limited number of numbers called the key risk indicators (KRIs), are used to describe the level of risk exposure. These risk exposure values, which are undeniably the outcome of a specific model, are frequently referred to as essential critical risk indicators. Five key risk indicators, including value-at-risk, tail variance, tail-value-at-risk, and tail mean-variance, were also used for describing the risk exposure under the reinsurance revenues data. These measurements were created for the proposed model; hence, this paper presents a novel distribution for this purpose. Relevant statistical properties are derived, including the generating function, ordinary moments, and incomplete moments. Special attention is devoted to the applicability of the new model under extreme data sets. Three applications to real data show the usefulness and adaptability of the proposed model. The new model proved its superiority against many well-known related models. Five key risk indicators are employed for analyzing the risk level under the reinsurance revenues dataset. An application is provided along with its relevant numerical analysis and panels. Some useful results are identified and highlighted. [ABSTRACT FROM AUTHOR]

The firm size distribution (FSD) is one of the most well-known economic empirical regularity in market economies. Its functional form, postulated in macroeconomic models with heterogeneous firms, can be approximated by a parametric distribution. However, the parametric approximations proposed in the literature have long been contested due to the lack of unbiased databases and robust statistical methods. This paper addresses these shortcomings. First, a robust estimation method is proposed to test the fit of parametric distributions and to determine the one offering the best fit at different truncation thresholds. Then, by applying it to a comprehensive database of Belgian firms for the period 2006–2012, the results show that the lognormal distribution is a better approximation of the empirical FSD than the Pareto distribution. These results hold true at the aggregate, sectoral and regional levels establishing that the shape of the aggregate distribution is not an aggregation artefact arising from the potential distributional heterogeneity of sectoral or regional subsets. This empirical evidence is essential information for tracing the root causes of a plausible underlying stochastic model explaining firm dynamics. [ABSTRACT FROM AUTHOR]

Abstract In this article, based on progressive type-II censored competing risks data with binomial removals, a constant-stress accelerated life testing is discussed when the lifetime of experiment units follows the Pareto distribution. Under the assumption that the failure time of each cause is statistically independent, the estimation of unknown parameters is obtained by maximum likelihood estimation and Bayesian estimators under symmetric and asymmetric loss functions. The corresponding confidence and credible intervals are constructed with approximation theory, bootstrap method, and MCMC technique respectively. Additionally, the log-linear model is established for the life test and two goodness-of-fit test statistics are constructed. Finally, a simulation study is carried out for the power analysis of different censoring ratio schemes and the numerical results verify the feasibility of the constructed test statistics for the censored data with competing risks. [ABSTRACT FROM AUTHOR]

We study two Bayesian (Reference Intrinsic and Jeffreys prior), two frequentist (MLE and PWM) approaches and the nonparametric Hill estimator for the Pareto and related distributions. Three of these approaches are compared in a simulation study and all four to investigate how much equity risk capital banks subject to Basel II banking regulations must hold. The Reference Intrinsic approach, which is invariant under one-to-one transformations of the data and parameter, performs better when fitting a generalized Pareto distribution to data simulated from a Pareto distribution and is competitive in the case study on equity capital requirements. [ABSTRACT FROM AUTHOR]

We investigate point estimation and confidence interval estimation for the heavy-tailed generalized Pareto distribution (GPD) based on the upper record values. When the shape parameter is known, the bias-corrected moments estimators and maximum likelihood estimators (MLE) for the location and scale parameters are derived. However, in practice, the shape parameter is typically unknown. We propose the MLE by a new methodological approach for all three parameters of the heavy-tailed GPD when the shape parameter is unknown. Confidence intervals for the location and scale parameters are constructed by the equal probability density principle. If the shape parameter is known, we can find known distributions of the pivots of the location and scale parameters, but not approximate. While if the shape parameter is unknown, the distributions of the pivots are closed linked to an estimation of the shape parameter. The advantage of our method is that the proposed interval estimation provides the smallest confidence interval, regardless of whether the distribution of the pivot is symmetric. Extensive simulations are used to demonstrate the performance of the point estimation and confidence intervals estimation and show that our method outperforms the traditional technique in most cases. [ABSTRACT FROM AUTHOR]

In this research, a single-server M-class retrial queueing system (orbit queue) with constant retrial rates and Poisson inputs is considered. The main purpose is to construct the upper and lower bounds of the stationary workload in this system expressed via the stationary workloads in the classical M / G / 1 systems where the service time has M-component mixture distributions. This analysis is applied to establish the extreme behaviour of stationary workload in the retrial system with Pareto service-time distributions for all classes. [ABSTRACT FROM AUTHOR]

In the present study, Flood Frequency Analysis (FFA) is performed on the daily inflows of a reservoir dam taken as a case study. The Peaks-Over-Threshold (POT) approach was adopted. A comparison between the default generalized Pareto distribution and the best distribution fitted to the data has been carried out. After the risk analysis, the reliability of the structure decreases to 25.60% for the chosen threshold values if the best distribution is adopted instead of the default fit. [ABSTRACT FROM AUTHOR]

The author examines competition prospects in the regulated market of a selected EU country to investigate specific policy choices. Under full market regulation, the actors have the exclusive right to deliver economic transactions. (1) Literature review: The theoretical part starts with the presentation of actors' heterogeneity and their market competition. (2) Methods: During empirical research, the author revised the cost structure and tested assumptions of the new trade theory of heterogenous firms and the impact of this heterogeneity on actors' competition. The author formed a three-step methodology where at the beginning, the actors are described, then a regression model is formulated, and volumes of delivered services are analyzed. In the end of this study, the author investigated if the costs of regulated market participants are characterized by the distribution of Pareto and analyzed the gaps between regulated prices and the level of costs. The author applied Pareto distribution and LS regression methods in the study. (3) Results: Although the author found that the market participants in the market concerned are very different, their distribution according to the Pareto distribution function could not be confirmed. (4) Conclusions: The study shows that competition prospects in a regulated market differ. This is proven by analyzing the impact of this heterogeneity on actors' competition. These results are essential in formulating the suggestion of economic policy. [ABSTRACT FROM AUTHOR]

The measure of entropy has a pivotal role in the information theory area. In this paper, estimation of differential entropy for Pareto distribution in presence of r outliers is considered. In this regard, the classical and Bayesian estimation techniques of differential entropy are employed. In classical setup, we obtain the maximum likelihood estimators of the differential entropy as well as assessing their performance via a simulation study. The entropy Bayesian estimator is derived using squared error, linear exponential, weighted squared error and K loss functions. The Metropolis-Hastings algorithm is used to generate posterior random variables. Monte Carlo simulations are designed to implement the precision of estimates for different sample sizes and number of outliers. Furthermore, performance of estimates is planned by experiments with real data. Generally, we conclude that the entropy Bayesian estimates of simulated data tend to the true value as the number of outliers increases. Further, the entropy Bayesian estimate under weighted squared error loss function is preferable to the other estimates in majority of situations. [ABSTRACT FROM AUTHOR]

Geochemical anomalies are the basis of mineral deposit prediction. Through the study of the characteristics of geochemical anomalies, we found that their distribution was consistent with a generalized Pareto distribution (GPD). In the present study, we designed a model for geochemical anomaly extraction via a GPD. In the designed GPD model, we used the kurtosis method to estimate the threshold value of the GPD. Furthermore, a principal component analysis (PCA) was used to extract comprehensive information of different geochemical elements in which minerals are enriched. On this basis, a new algorithm named the GPDA model was designed for deep mineral prediction by using the GPD and PCA, and the methods of the GPDA for selecting parameters were studied. The study data for Ba, Pb, As, Cu, Au, Mo, Co, and Zn originated from 26 exploration lines of the Jiguanzui Cu-Au mining area in Hubei, China. The proposed GPDA model was applied to deep mineral prediction in the study area. We estimated the parameters of the GPDA model, and the thresholds of Ba, Pb, As, Cu, Au, Mo, Co, and Zn were 457.8612, 56.1823, 28.8454, 910.1272, 89.4283, 34.5267, 84.9445, and 121.4863, respectively. The comprehensive information threshold value was 0.4551. The comprehensive abnormal distribution area of geochemical element contents was obtained from thresholds. The results showed that the method used to identify abnormal areas was consistent with the range of ore bodies identified by actual engineering exploration, demonstrating that the GPDA model was effective. Finally, we predicted that there was a new blind ore body located at a depth of about 1100 m below ground between drill holes KZK10 and KZK11. The results have important theoretical and practical significance for deep ore prospecting. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a robust estimator of the tail index of a Pareto-type distribution. The estimator is obtained through the use of the minimum density power divergence with an exponential regression model for log-spacings of top order statistics. The proposed estimator is compared to existing minimum density power divergence estimators of the tail index based on fitting an extended Pareto distribution and exponential regression model on log-ratio of spacings of order statistics. We derive the influence function and gross error sensitivity of the proposed estimator of the tail index to study its robustness properties. In addition, a simulation study is conducted to assess the performance of the estimators under different contaminated samples from different distributions. The results show that our proposed estimator of the tail index has better mean square errors and is less sensitive to an increase in the number of top order statistics. In addition, the estimation of the exponential regression model yields estimates of second-order parameters that can be used for estimation of extreme events such as quantiles and exceedance probabilities. The proposed estimator is illustrated with practical datasets on insurance claims and calcium content in soil samples. [ABSTRACT FROM AUTHOR]

Due to the atmospheric temperature and solar radiation, the effects of temperature variation in bridge structures should be considered. Such variation induces notable deformations and movements, jeopardizing the safety of bridges and high-speed trains operations. However, the temperature action is a random process and its distribution is difficult to determine. The existing methods for analyzing structural temperatures are insufficient to meet the precision requirement. Therefore, the accurate prediction of extreme structural temperatures relates to the accurate evaluation on the bridge safety. This paper proposes a robust and accurate model for predicting the extreme structural temperature of a bridge. A field experiment, spanning over 2 years, was carried out on a high-speed railway bridge; and the long-term (56-years) atmospheric temperature data was adopted. Probabilistic models for the structural temperature were established using the Maximum Entropy (MaxEnt) model and the Generalized Pareto distribution (GPD) model; and the predictions on the uniform structural temperature (T u ) with 50 and 100 years return periods are presented. Additionally, the performance between the MaxEnt model and the GPD model is compared, based on the estimates with different return levels. The results show that the MaxEnt model is more stable and is significantly robust to the variation of sample sizes; and indicates that the MaxEnt model reduces the uncertainty of outcomes and avoids the high risk of bias. The MaxEnt model has a great potential to the applications of the extreme value analysis with small sample size. It offers a wider applicability and helps solve practical problems. [ABSTRACT FROM AUTHOR]

In this study, biopolymer chitosan is presented as a template for synthesizing and shaping the mesoporous γ‐Al2O3 macrospheres. This porous γ‐Al2O3 granule has a high surface area (310 m2/g), high pore volume (.6148 cm3/g), and pore diameter between 2 and 10 nm. The full factorial design based on a mathematical model was implemented to study the acid concentration, chitosan amount, ammonia concentration, and aging time affecting the responses (Brunauer–Emmett–Teller surface area and pore volume). Predicted responses were found to be in satisfactory agreement with experimental values (R2 =.9580 and.9109, respectively). The adequacy of the model was examined by analyzing the residual distribution plots and Pareto graph. X‐ray diffraction, scanning electron microscopy (SEM), thermogravimetric analysis, and N2 adsorption/desorption techniques are employed to characterize the structure of the prepared γ‐alumina sample. [ABSTRACT FROM AUTHOR]

This paper provides a meta-heuristic hybridized version called multi-objective golden flower pollination algorithm (MOGFPA) as the best method for choosing the optimal reconfiguration for distribution networks (DNs) in order to reduce power losses (PLs). Aside from PLs, another parameter is considered: the load balance index (LBI). The expression for the LBI is stated using real and reactive indices. It makes the optimal distributed generation (DG) placement and DN routing of the multi-objective (MO) problem have PLs and the LBI as the main parameters that need to be optimized. For that purpose, the MOGFPA is proposed in this paper. The MOGFPA consists of a golden search (GS) and tangent flight with Pareto distribution that only needs a few tuning parameters. Therefore, it is simple to alter these parameters to reach the best values compared to other existing methodologies. Its performance is predicted using different case studies on multiple test bus systems, namely the IEEE systems such as 33, 69, 119, and Indian 52 bus. Through simulation outcomes, the MOGFPA computes the optimum distribution of DG units and reconfigures the DNs with the aim of minimal PLs and LBI. Furthermore, another state-of-the-art technology and comparing convergence charts provide optimal outputs in less time, with minimum iterations. [ABSTRACT FROM AUTHOR]

This article proposes an open-set recognition model that is based on the use of extreme value statistics. For this purpose, a distance ratio is introduced that expresses how dissimilar a target point is from the known classes by considering the ratio of distances locally around the target point. It is shown that the class of generalized Pareto distributions with bounded support can be used to model the peaks of the distance ratio above a high threshold. The resulting distribution provides a probabilistic framework to perform open-set recognition. Furthermore, we describe a numerical procedure to estimate the hyperparameters of our model. This procedure is based on a new objective function that considers both the fit of the generalized Pareto distribution and the misclassification error of the known classes. Our method is applied to three image datasets and an audio dataset showing that it outperforms similar open-set recognition and anomaly detection methods. for this article are available online. [ABSTRACT FROM AUTHOR]

• Short-term electricity generation data is used to calculate PGF for Khartoum. • Peaks over threshold method is utilized to model the highest power generation. • The obtained PGF equals 4, whereas in PV potential map equals 4.8. • This factor shall facilitate PV system sizing for local engineers. In this research, the authors used the Peaks over Threshold (POT) method alongside short-term electricity generation data belonging to a 5.5 kW p off-grid photovoltaic (PV) system installed on the premises of the National Energy Research Center in Soba district, Khartoum, to estimate the panel generation factor (PGF) of the city that rests within Sudan's capital. PGF is a fundamental technical figure primarily used in the design/sizing of solar PV systems. The addressed problem here is to calculate this coefficient with an acceptable accuracy constrained by insufficient electricity generation data from a PV system operating at its maximum capacity, relying on statistical modeling methods, which is the research novelty. Accordingly, we obtained an approximate PGF of 4 utilizing the POT technique that resulted in a threshold of 19 and Generalized Pareto distribution estimators of 2.2 × 10 - 16 and 2.3 for the shape and scale parameters, respectively. In the literature, the corresponding factor value is 4.8, illustrated in Sudan's PV potential map, based on historical long-term solar irradiance satellite records. Consequently, a 16.67% Percent Error between the two values is present due to the big difference in data amount, favoring the literature. However, in front of relatively abundant data, we believe the Extreme Value Theory methodology applied here will demonstrate robustness in approximating the target factor digits and validating Sudan's map numbers. Finally, this effort shall enable local engineers to blueprint well-assessed PV systems and support the endeavors to scientifically document Sudan's PV energy capacity, which the country lacks very much. [ABSTRACT FROM AUTHOR]

We propose a new metaheuristic, HmGWOGA-MO, for solving multiobjective optimization problems operating with a population of solutions. The method is a hybridization of the HmGWOGA method, which is a single objective optimization method, and the ϵ-constraint approach, which is an aggregation technique. The ϵ-constraint technique is one of the best ways to transform a problem with many objective functions into a single objective problem because it works even if the problem has any kind of Pareto optimal front. Previously, the HmGWOGA method was designed to optimize a positive single-objective function without constraints. The obtained solutions are good. That is why, in this current work, we combined have it with the ϵ-constraint approach for the resolution of multiobjective optimization problems. Our new method proceeds by transforming a given multiobjective optimization problem with constraints into an unconstrained optimization of a single objective function. With the HmGWOGA method, five different test problems with varying Pareto fronts have been successfully solved, and the results are compared with those of NSGA-II regarding convergence towards the Pareto front and the distribution of solutions on the Pareto front. This numerical study indicates that HmGWOGA-MO is the best choice for solving a multiobjective optimization problem when convergence is the most important performance parameter. [ABSTRACT FROM AUTHOR]

Aim: Invasive alien species are a growing problem worldwide due to their ecological, economic and human health impacts. The "killer shrimp" Dikerogammarus villosus is a notorious invasive alien amphipod from the Ponto‐Caspian region that has invaded many fresh and brackish waters across Europe. Understandings of large‐scale population dynamics of highly impactful invaders such as D. villosus are lacking, inhibiting predictions of impact and efficient timing of management strategies. Hence, our aim was to assess trends and dynamics of D. villosus as well as its impacts in freshwater rivers and streams. Location: Europe. Methods: We analysed 96 European time series between 1994 and 2019 and identified trends in the relative abundance (i.e. dominance %) of D. villosus in invaded time series, as well as a set of site‐specific characteristics to identify drivers and determinants of population changes and invasion dynamics using meta‐regression modelling. We also looked at the spread over space and time to estimate the invasion speed (km/year) of D. villosus in Europe. We investigated the impact of D. villosus abundance on recipient community metrics (i.e. abundance, taxa richness, temporal turnover, Shannon diversity and Pielou evenness) using generalized linear models. Results: Population trends varied across the time series. Nevertheless, community dominance of D. villosus increased over time across all time series. The frequency of occurrences (used as a proxy for invader spread) was well described by a Pareto distribution, whereby we estimated a lag phase (i.e. the time between introduction and spatial expansion) of approximately 28 years, followed by a gradual increase before new occurrences declined rapidly in the long term. D. villosus population change was associated with decreased taxa richness, community turnover and Shannon diversity. Main Conclusion: Our results show that D. villosus is well‐established in European waters and its abundance significantly alters ecological communities. However, the multidecadal lag phase prior to observed spatial expansion suggests that initial introductions by D. villosus are cryptic, thus signalling the need for more effective early detection methods. [ABSTRACT FROM AUTHOR]

The Pareto Distribution has been found to be useful in describing socio-economic, physical, and biological phenomena. This paper explores different methods of estimating the shape parameter of the Pareto distribution and two of its functions (reliability and hazard functions), assuming the scale parameter is known. In particular, this paper shows that the Bayesian approach, using both the quadratic and entropy loss functions, can provide a general method for estimating the shape parameter and these two functions. These Bayesian estimators generalize the maximum likelihood estimator (MLE) and the uniformly most powerful unbiased estimator (UMVUE). Simulation results show that the general Bayesian method can perform better than the MLE and UMVUE, especially when the sample size is small. [ABSTRACT FROM AUTHOR]

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Reducing uncertainty in design flood estimates is an essential part of flood risk planning and management. This study presents results from flood frequency estimates and associated uncertainties for five commonly used probability distribution functions, extreme value type 1 (EV1), generalized extreme value (GEV), generalized pareto distribution (GPD), log normal (LN) and log Pearson type 3 (LP3). The study was conducted using Monte Carlo simulation (MCS) and bootstrapping (BS) methods for the 10 river catchments in eastern Australia. The parameters were estimated by applying the method of moments (for LP3, LN, and EV1) and L-moments (for GEV and GPD). Three-parameter distributions (e.g., LP3, GEV, and GPD) demonstrate a consistent estimation of confidence interval (CI), whereas two-parameter distributions show biased estimation. The results of this study also highlight the difficulty in flood frequency analysis, e.g., different probability distributions perform quite differently even in a smaller geographical area. [ABSTRACT FROM AUTHOR]

Mixture distributions play an important role in many studies in real time scenario. It has many applications to name some of them are: Insurance risk theory, oil industry, reliability theory etc. Mixture distributions are probability distributions of a random variable, derived from the convex combination of individual distributions as components of the random variable, with the corresponding proportion of each component called as the mixture weights. In this paper, an attempt is made to propose a new mixture distribution, using three Pareto distributions with different fixed proportions. The properties of the distribution are also derived and presented. [ABSTRACT FROM AUTHOR]

Effective indoor testing on a four-poster rig of agricultural machinery should mimic the real-world environment while the machinery is in farming and transportation. The emerging load spectrum extrapolation and compilation are capable of speeding up the use of the indoor vibration testing of tractors. However, most ground load spectrum studies consider a particular type of ground rather than all the rough farmland conditions that tractors experience daily. Such a problem inevitably raises doubts about validating the load spectrum-based fatigue durability and reliability testing of tractors. For a remedy, this article proposes a CEEMDAN-POT (Peak Over Threshold) model to comprehensively build a full life-cycle ground load spectrum of tractor vibration with six ground conditions and different field operations. The study acquires the real four vertical acceleration signals from the front and rear axles of the tractor to collect representative vibration load data. Furthermore, the study refines the measured load data by proposing a CEEMDAN-Wavelet threshold method, which is proved to be effective for the load signal decomposition and denoising. Lastly, the study presents a time domain extrapolation method, integrating the sample principle of the POT model, the proper parameter estimation with the Generalized Pareto Distribution (GPD) function, and the POT super-threshold model. The statistical analysis implies that the produced load spectrum fully preserves the statistical features observed in the original one. After extrapolation, the overall distribution of the rainflow matrix becomes more consistent while the mean and amplitude of the spectrum data increase. This study unifies a load spectrum of tractors operating and transporting on various farm ground conditions, providing the real load data of the indoor four-poster rig test. [ABSTRACT FROM AUTHOR]

In 2019, a new lethal and mutant virus (COVID-19) spread around the world, causing the deaths of millions of people. COVID-19 demonstrates that scientists are involved in significant research efforts to face bacteria with less effort than that dedicated to viruses. Since then, engineers and bio-materials scientists have been trying to develop antiviral research and find a suitable effective medication. Strategies and opportunities for interference diagnostics, treatment strategies, and predicting future factors became mandatory. From a statistical point of view, estimating and modelling these factors play an important role in preventing future viral epidemics. In this article, modelling the recovery rate of COVID-19 is investigated through a new distribution which is called the unit exponential Pareto distribution. The new continuous distribution with three parameters displays a prominent level of flexibility to model decreasing, symmetric, and asymmetric data with a monotone failure rate. The recovery rates of COVID-19 in Turkey and France were examined; moreover, milk production data and components' failure rates are presented for data modeling. The obtained results proved the superiority of the newly suggested model compared to other unit-based distributions. Several statistical features are studied such as the quantile function, the moments, the moment-generating function, some entropy measures, the ordered statistics, the stress–strength, and stochastic ordering. Two classical estimation methods are used in addition to the Bayesian method. The statistical features and estimation analysis are evaluated using numerical and simulation techniques. As a result, we obtain the efficiency of using the Bayesian method over the classical ones, with respect to the bias, average squared error, and the length of confidence intervals for the unknown parameters. [ABSTRACT FROM AUTHOR]

We study a model of over-the-counter trading in which ex ante identical traders invest in a contact technology and participate in bilateral trade. We show that a rich market structure emerges both in equilibrium and in an optimal allocation. There is continuous heterogeneity in market access under weak regularity conditions. If the cost per contact is constant, heterogeneity is governed by a power law and there are middlemen, market participants with unboundedly high contact rates who account for a positive fraction of meetings. Externalities lead to overinvestment in equilibrium, and policies that reduce investment in the contact technology can improve welfare. We relate our findings to important features of real-world trading networks. [ABSTRACT FROM AUTHOR]