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AbstractBetween the two world wars, a group of Italian mathematicians, statisticians and economists set out to use the tools of statistical mechanics to interpret the Pareto income distribution curve as a probability distribution. Models based on Boltzmann's thermal equilibrium were independently developed to find an economic variable, comparable to the kinetic energy of gas theory, that could explain the heavy tail of the Pareto curve. The various avenues explored eventually led them back to Pareto's much debated explanation, namely that the hyperbolic distribution of income was due to the unequal distribution of talent. [ABSTRACT FROM AUTHOR]

In the present age of industrial revolution where the smart manufacturing and smart production are being used in the developed countries, the production systems are still vulnerable to disruptions and outages that affect the reliability and availability of the systems. Certain scientific and probabilistic approaches are required to study the inter‐failure times and repair times and find the possible solutions for maximum production and minimum losses. In this article, we propose a bivariate Power Pareto distribution to model the inter‐failure times and repair times of a system along with some of its characteristics. The model parameters are estimated by employing the maximum likelihood estimation, Bayesian estimation and ant colony optimization algorithm. A simulation study is conducted for different sample sizes to assess the stability of the model parameters. Moreover, we derive the distribution of convolution from our proposed bivariate stochastic distribution and compute its quantiles that help to determine the total time of availability and recovery of a certain system. To demonstrate the efficacy of our model, we use real data set of inter‐failure times and repair times of a certain system. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of generalized conditional spacings and establishes partial order relations between different generalized spacings. First, we derive the survival function of the generalized conditional spacings. Second, we construct the stochastic and hazard rate order relationships between different generalized conditional spacings and generalized normal conditional spacings, considering parent distributions that belong to the decreasing failure rate (DFR) and increasing likelihood rate (ILR) classes. Finally, for parent distributions within the DFR class, we obtain the dispersive order between different conditional spacings, along with an inequality for the variance. Additionally, we present illustrative examples involving Pareto and Gamma distributions. [ABSTRACT FROM AUTHOR]

In this study, data from 23 domestic cremation facilities measured for 5 years (from 2016 to 2020) of 13 domestic cremation facilities was used to calculate the emission factors of dioxins (PCDD/DFs) of cremation facilities that use Liquified Natural Gas (LNG) as combustion fuel. We performed a statistical analysis for the first time to estimate the emission factor using limited measurement results from cremation facilities that are not easily accessible. We attempted to identify the emission concentration of dioxin as a representative persistent organic pollutants substance and developed a statistically based dioxin emission factor. The concentration of dioxins (PCDD/DFs) in the cremation facility ranged 0.001–4.440 ng I-TEQ/Sm3 with an average concentration of 0.719 ng I-TEQ/Sm3. The emission factor calculated using the 23 measured data showed 0.010–21.485 μg I-TEQ/Cremation. A Monte Carlo Simulation was conducted using probability density distribution and parameter estimation. Consequently, 10,000 emission factors were selected, and the Pareto distribution was predicted to be the most appropriate probability density distribution. The emission factor values through Monte Carlo simulation showed a minimum value of 1.490 × 10–08 μg I-TEQ/Cremation and a maximum value of 7816 μg I-TEQ/Cremation. The average value was calculated as 39.920 μg I-TEQ/Cremation. Each parameter of the Pareto distribution is shape parameter (α) 1.026, location parameter (μ) – 1.021, and scale parameter (λ) 1.021. As a result of this study, the median value of the cumulative density function was selected as a representative value for the dioxin emission factor of cremation facilities and the emission factor was 0.986 μg I-TEQ/ Cremation. The 95% confidence interval in the Pareto distribution was presented as 0.026 μg I-TEQ/Cremation to 36.216 μg I-TEQ/ Cremation. [ABSTRACT FROM AUTHOR]

This paper derives finite sample results to assess the consistency of Generalized Pareto regression trees introduced by Farkas et al. (Insur. Math. Econ. 98:92–105, 2021) as tools to perform extreme value regression for heavy-tailed distributions. This procedure allows the constitution of classes of observations with similar tail behaviors depending on the value of the covariates, based on a recursive partition of the sample and simple model selection rules. The results we provide are obtained from concentration inequalities, and are valid for a finite sample size. A misspecification bias that arises from the use of a "Peaks over Threshold" approach is also taken into account. Moreover, the derived properties legitimate the pruning strategies, that is the model selection rules, used to select a proper tree that achieves a compromise between simplicity and goodness-of-fit. The methodology is illustrated through a simulation study, and a real data application in insurance for natural disasters. [ABSTRACT FROM AUTHOR]

In this paper, a class of fractional multiobjective interval valued optimization problems with Einvexity is considered. First, the definition of the E-invex fractional interval value function is given under the interval order relation, and the existence of these fractional interval-valued functions is verified by examples. Second, we present the E-KKT necessary optimality conditions and the sufficient optimality conditions for a fractional interval-valued optimization problem (FIVPE) under E-invexity. Last, the Mond-Weir E-dual problem (DFIVPE) of (FIVPE) is established, and several E-duality theorems are obtained under E-invexity. To some extent, this paper generalizes the existing relevant results obtained recently. [ABSTRACT FROM AUTHOR]

I derive a stationary distribution of lifetime wealth accumulation factor in a model featuring inheritance of productivity, wealth, and health condition, where lifetime wealth is the sum of financial wealth and human wealth. Assuming ex-ante heterogeneity in the death rate, I show that the distribution of the lifetime wealth accumulation factor is constituted by a weighted sum of shape-differing Pareto distributions. It is shown that raising the wealth tax reduces inequality of lifetime wealth not only within a death-rate type but also across all the death-rate types. [ABSTRACT FROM AUTHOR]

Income and wealth surveys are usually affected by unit non‐response and reporting errors, which contribute to a mismatch with macroeconomic figures from national accounts. In this paper, we develop a novel allocation method to address these two issues simultaneously, when only limited external information is available. The proposed approach combines information from a power law (Pareto) model with imputation procedures based on calibration. We apply the proposed simultaneous approach to produce distributional indicators for four Euro‐Area countries that are consistent with their national accounts. In particular, we use data from the 2014 Finnish, French, German, and Italian Household Finance and Consumption Survey and rich list data from Forbes or national press sources, along with household sector aggregates from national accounts, as auxiliary sources of information. A bootstrap procedure is also applied to evaluate the precision of the final estimates. [ABSTRACT FROM AUTHOR]

A fast multi-objective optimization method (FMOOM) is proposed by optimizing control parameters to improve the dynamic performance of a high-speed maglev vehicle–bridge system. This approach involves generating the corresponding dynamic response to the sampled control parameters using a theoretical model of a high-speed maglev vehicle–bridge system, followed by establishing an adaptive surrogate model for the relationship between the control parameters and the dynamic response extrema. In the second step, we combine the adaptive surrogate model and the multi-objective gradient-based optimizer (MOGBO) algorithm to obtain the Pareto solution set satisfying different performance indexes. Additionally, the control parameters are optimized using the fuzzy comprehensive evaluation method. In the numerical simulation, we investigate five maglev trains and ten-span simply supported beam bridges and the theoretical model is verified by comparing the calculations with the measured results. The optimization effect of FMOOM is analyzed under different working conditions. The results show that the adaptive surrogate model has good prediction accuracy based on the radial basis function. Furthermore, the Pareto solution distribution of different schemes using FMOOM is reasonable, and the optimization results are as expected. Compared with the reference scheme, the dynamic response of the maglev vehicle–bridge system is smaller after being subjected to FMOOM optimization, and the six performance indexes are dramatically improved. [ABSTRACT FROM AUTHOR]

Recently, the need to develop statistical distributions has become the most important spot. In this context, we employ the α‐power transformation (APT) method to convert the generalized Pareto distribution (GPD) into a new distribution. Some statistical properties of the proposed distribution are being studied, such as moments, arithmetic mean, moment‐generating function, random variables, entropy, reliability, and hazard function (HF). In addition, the proposed distribution is compared with the Pareto distribution and some other forms of alpha power distributions, such as the alpha power Pareto (APP) distribution, alpha power Rayleigh (APR) distribution, and the alpha power Lomax (APL) distribution. Finally, we demonstrate the benefits of the proposed distribution through a simulation study and two real data sets. It was found that the results showed the MLE method is reliable, the APTGP distribution is a competitive distribution for the aforementioned data set, and it is a mirror image of the Pareto distribution. [ABSTRACT FROM AUTHOR]

Simple Summary: This study aimed to examine the aging process of fibrous elements in the dermis of male volunteers over a 10-year period (47–57 years). It was observed that the aging process included visible changes in the content and organization of type I collagen fibers, resulting in changes in fibroblast morphology, and changes in type III collagen and elastic fibers. For the first time, this study presents a comparison of the dynamics of changes in morphology of the dermis in the same volunteer over a time interval of 10 years. Skin aging is a complex phenomenon influenced by multiple internal and external factors that can lead to significant changes in skin structure, particularly the degradation of key extracellular matrix (ECM) components such as collagen and elastic fibers in the dermis. In this study, we aimed to meticulously assess the morphological changes within these critical fibrous ECM elements in the dermis of the same volunteer at age 47 and 10 years later (2012 to 2022). Using advanced histological staining techniques, we examined the distribution and characteristics of ECM components, including type I collagen, type III collagen, and elastic fibers. Morphological analysis, facilitated by hematoxylin and eosin staining, allowed for an accurate assessment of fiber bundle thickness and a quantification of collagen and elastic fiber areas. In addition, we used the generalized Pareto distribution for histogram modeling to refine our statistical analyses. This research represents a pioneering effort to examine changes in ECM fiber material, specifically within the male dermis over a decade-long period. Our findings reveal substantial changes in the organization of type I collagen within the ECM, providing insight into the dynamic processes underlying skin aging. [ABSTRACT FROM AUTHOR]

This article presents a mixed Pareto model and examines its suitability for modeling non life insurance claim severity data sets which exhibit peculiar characteristics that cannot be captured by the Pareto distribution. Furthermore, we introduce regression specifications for both the mean and the dispersion parameters of the mixed Pareto model. Our main achievement is that we develop a novel Expectation-Maximization (EM) algorithm for finding the maximum likelihood (ML) estimates of the parameters of the mixed Pareto regression model which is used for demonstration purposes. Finally, a real-data application based on motor insurance claim size data is provided. [ABSTRACT FROM AUTHOR]

Exploring the stochastic intricacies of bone microstructure is a promising way to make progress on the practical issue of bone fracture. This study investigates the fracture of human complete ribs subjected to bending and using acoustic emission (AE) for microfailure detection. As the strain increases, the number of AE signals per unit of time rises until, beyond a certain threshold, an avalanche of signals occurs, indicating the aggregation of numerous microfailures into a macroscopic fracture. Since microfailures appear randomly throughout the bending test, and given the lack of a deterministic law and the random nature of microfailures during the bending test, we opted to develop a stochastic model to account for their occurrence within the irregular and random microstructure of the cortical bone. Notable discoveries encompass the significant correlation between adjusted parameters of the stochastic model and the total number of microfailures with anthropometric variables such as age and body mass index (BMI). The progression of microfailures with strain is significantly more pronounced with age and BMI, as measured by the rate of bone deterioration. In addition, the rate of microfailures is significantly impacted by BMI alone. It is also observed that the average energy of the identified AE events adheres to a precisely defined Pareto distribution for every specimen, with the principal exponent exhibiting a significant correlation with anthropometric variables. From a mathematical standpoint, the model can be described as a double Cox stochastic and explosive (coxplosive process) model. This further provides insight into the reason why the ribs of older individuals are considerably less resilient than those of younger individuals, breaking under a considerably lower maximum strain ( ε max ). [ABSTRACT FROM AUTHOR]

Flood frequency analysis at large scales, essential for the development of flood risk maps, is hindered by the scarcity of gauge flow data. Suitable methods are thus required to predict flooding in ungauged basins, a notoriously complex problem in hydrology. We develop a Bayesian hierarchical model (BHM) based on the generalized extreme value (GEV) and the generalized Pareto distribution for regional flood frequency analysis at high resolution across a large part of North America. Our model leverages annual maximum flow data from ≈20,000 gauged stations and a dataset of 130 static catchment-specific covariates to predict extreme flows at all catchments over the continent as well as their associated statistical uncertainty. Additionally, a modification is made to the data layer of the BHM to include peaks over threshold flow data when available, which improves the precision of the discharge level estimates. We validated the model using a hold-out approach and found that its predictive power is very good for the GEV distribution location and scale parameters and improvable for the shape parameter, which is notoriously hard to estimate. The resulting discharge return levels yield a satisfying agreement when compared with the available design peak discharge from various government sources. The assessment of the covariates' contributions to the model is also informative with regard to the most relevant underlying factors influencing flood-inducing peak flows. According to the developed aggregate importance score, the key covariates in our model are temperature-related bioindicators, the catchment drainage area and the geographical location. [ABSTRACT FROM AUTHOR]

The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log‐log scale. Nevertheless, there have been criticisms of the power law, for example, that a threshold needs to be preselected without its uncertainty quantified, that the power law is simply inadequate, and that subsequent hypothesis tests are required to determine whether the data could have come from the power law. We propose a modeling framework that combines two different generalizations of the power law, namely the generalized Pareto distribution and the Zipf‐polylog distribution, to resolve these issues. The proposed mixture distributions are shown to fit the data well and quantify the threshold uncertainty in a natural way. A model selection step embedded in the Bayesian inference algorithm further answers the question whether the power law is adequate. [ABSTRACT FROM AUTHOR]

Delays in nerve transmission are an important topic in the field of neuroscience. Spike signals fired or received by the dendrites of a neuron travel from the axon to a presynaptic cell. The spike signal then triggers a chemical reaction at the synapse, wherein a presynaptic cell transfers neurotransmitters to the postsynaptic cell, regenerates electrical signals via a chemical reaction through ion channels, and transmits them to neighboring neurons. In the context of describing the complex physiological reaction process as a stochastic process, this study aimed to show that the distribution of the maximum time interval of spike signals follows extreme-order statistics. By considering the statistical variance in the time constant of the leaky Integrate-and-Fire model, a deterministic time evolution model for spike signals, we enabled randomness in the time interval of the spike signals. When the time constant follows an exponential distribution function, the time interval of the spike signal also follows an exponential distribution. In this case, our theory and simulations confirmed that the histogram of the maximum time interval follows the Gumbel distribution, one of the three forms of extreme-value statistics. We further confirmed that the histogram of the maximum time interval followed a Fréchet distribution when the time interval of the spike signal followed a Pareto distribution. These findings confirm that nerve transmission delay can be described using extreme value statistics and can therefore be used as a new indicator of transmission delay. [ABSTRACT FROM AUTHOR]

Climate change and climate variation influence the occurrence of natural disasters, especially water-related disasters. Landslides are a serious hydrogeohazard in Thailand. Hence, this study aims to project the spatial changes in the landslide susceptibility area in the Nakhon Si Thammarat province of southern Thailand. The study utilizes five climate models of CMIP6 (INM-CM4-8, IITM-ESM, MPI-ESM1-2-LR, CNRM-ESM2-1 and CNRM-CM6.-1) and conducts analyses based on 2 shared socioeconomic pathways (SSPs) of tier 1, which include SSP2-4.5 and SSP5-8.5. The linear scaling bias correction technique is applied to adjust for any biases in the climate models, and the model results are combined using the ensemble mean method. To achieve the study aims, a GIS-aided physically based landslide susceptibility model is used to predict changes in spatial aspects of the landslide susceptibility area. The analysis predicted spatial changes in the landslide susceptibility area over the next 20 years (2023 to 2042). According to the analysis, the results showed that the maximum increase in landslide susceptibility areas is approximately 29%, and the maximum decrease in landslide susceptibility areas is approximately 25% under SSP2-4.5. For SSP5-8.5, the maximum increase in landslide susceptibility areas is approximately 31%, and the maximum decrease in landslide susceptibility areas is approximately 35%. Moreover, the fluctuation of rainfall strongly influences the increase or decrease in landslide susceptibility areas. However, the landslide-prone areas remain located in areas that have experienced landslides in the past. [ABSTRACT FROM AUTHOR]

We introduce a novel technique for producing several families of distributions: the alpha-log-power transformed method. The novelty of our new approach lies in the fact that it adds one new shape parameter and was not derived from any established parent model. Some examples of the new family are presented. Also, some important statistical properties of the new family are studied. The maximum likelihood estimation approach is utilized to estimate the model parameters of the new family. To evaluate the performance of the estimators, Monte Carlo simulation is conducted using some arbitrary baseline distributions namely the Weibull, Burr-XII and Pareto distribution. Two real datasets are used to empirically show the potential significance and applicability of the alpha log power transformed Weibull. The alpha log power transformed Weibull is a very competitive model for characterizing observations in survival analysis. [ABSTRACT FROM AUTHOR]

We propose a dynamic semiparametric framework to study time variation in tail parameters. The framework builds on the Generalized Pareto Distribution (GPD) for modeling peaks over thresholds as in Extreme Value Theory, but casts the model in a conditional framework to allow for time-variation in the tail parameters. We establish parameter regions for stationarity and ergodicity and for the existence of (unconditional) moments and consider conditions for consistency and asymptotic normality of the maximum likelihood estimator for the deterministic parameters in the model. Two empirical datasets illustrate the usefulness of the approach: daily U.S. equity returns, and 15-min euro area sovereign bond yield changes. [ABSTRACT FROM AUTHOR]

Coastal regions face increasing threats from rising sea levels and extreme weather events, highlighting the urgent need for accurate assessments of coastal flood risk. This study presents a novel approach to estimating global extreme sea level (ESL) exceedance probabilities using a regional frequency analysis (RFA) approach. The research combines observed and modelled hindcast data to produce a high-resolution (∼1 km) dataset of ESL exceedance probabilities, including wave setup, along the entire global coastline (excluding Antarctica). The methodology presented in this paper is an extension of the regional framework of Sweet et al. (2022), with innovations introduced to incorporate wave setup and apply the method globally. Water level records from tide gauges and a global reanalysis of tide and surge levels are integrated with a global ocean wave reanalysis. Subsequently, these data are regionalised, normalised, and aggregated and then fit with a generalised Pareto distribution. The regional distributions are downscaled to the local scale using the tidal range at every location along the global coastline obtained from a global tide model. The results show 8 cm of positive bias at the 1-in-10-year return level when compared to individual tide gauges. The RFA approach offers several advantages over traditional methods, particularly in regions with limited observational data. It overcomes the challenge of short and incomplete observational records by substituting long historical records with a collection of shorter but spatially distributed records. These spatially distributed data not only retain the volume of information but also address the issue of sparse tide gauge coverage in less populated areas and developing nations. The RFA process is illustrated using Cyclone Yasi (2011) as a case study, demonstrating how the approach can improve the characterisation of ESLs in regions prone to tropical cyclone activity. In conclusion, this study provides a valuable resource for quantifying the global coastal flood risk, offering an innovative global methodology that can contribute to preparing for – and mitigating against – coastal flooding. [ABSTRACT FROM AUTHOR]

• This study introduce extreme value theory (EVT) and Peaks Over Threshold (POT) methods into the calculation of takeover time thresholds; a methodology for calculating and verifying takeover time thresholds has been developed. • This study calculated the takeover time thresholds of drivers with different attributes, which can provide support for differentiated management of driver qualifications. • This study can also support regulatory authorities to assess the driver's takeover response ability and support the responsibility division of automated vehicle accidents. In conditional automated driving, the takeover response ability threshold is necessary for driver qualification assessment and liability division of automated vehicle accidents. The primary objective of this study is to establish a clear and quantifiable threshold for drivers' takeover response ability in conditional automated driving scenarios. This threshold aims to serve as a benchmark for evaluating drivers' readiness and developing safety regulations in automated driving. We designed 18 takeover events and invited 42 drivers to participate in the driving simulation experiment, and obtained their takeover time data. First, we analyze the differences of takeover time among drivers with different attributes (gender, age, driving year). Second, based on the Peaks Over Threshold and the generalized Pareto distribution model, we use the graphic method to calculate the range of takeover time threshold for drivers with different attributes. The result shows that the difference in the threshold range of takeover time between male and female drivers is relatively tiny. There are differences in the threshold range of takeover time for different age drivers, and the threshold is negatively correlated with age. Drivers with high driving experience within a safe range are allowed to have longer takeover times. Finally, the rationality of the takeover time threshold for drivers with different attributes has been verified. The return level curves are approximately linear (R2 > 0.77), indicating that the GPD model can capture the overall trend of the return level, which is changing with the probability level. This proves that the takeover time threshold is reasonable. This study uses TTC min to calibrate takeover safety, and the takeover time threshold has a good classification performance for takeover safety (accuracy > 85 %). The above content proves the rationality of the takeover time threshold. The contribution of this study is to calculate the takeover time threshold of drivers with different attributes, which can help regulatory authorities assess the driver's takeover response ability and support the liability division of automated vehicle accidents. [ABSTRACT FROM AUTHOR]

AbstractThe severity of multivariate extreme events is driven by the dependence between the largest marginal observations. The Hüsler–Reiss distribution is a versatile model for this extremal dependence, and it is usually parameterized by a variogram matrix. In order to represent conditional independence relations and obtain sparse parameterizations, we introduce the novel Hüsler–Reiss precision matrix. Similarly to the Gaussian case, this matrix appears naturally in density representations of the Hüsler–Reiss Pareto distribution and encodes the extremal graphical structure through its zero pattern. For a given, arbitrary graph we prove the existence and uniqueness of the completion of a partially specified Hüsler–Reiss variogram matrix so that its precision matrix has zeros on non-edges in the graph. Using suitable estimators for the parameters on the edges, our theory provides the first consistent estimator of graph structured Hüsler–Reiss distributions. If the graph is unknown, our method can be combined with recent structure learning algorithms to jointly infer the graph and the corresponding parameter matrix. Based on our methodology, we propose new tools for statistical inference of sparse Hüsler–Reiss models and illustrate them on large flight delay data in the United States, as well as Danube river flow data. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

We propose new classes of goodness-of-fit tests for the Pareto Type I distribution. These tests are based on a characterization of the Pareto distribution involving order statistics. We derive the limiting null distribution of the tests and also show that the tests are consistent against fixed alternatives. The finite-sample performance of the newly proposed tests are evaluated and compared to some of the existing tests, where it is found that the new tests are competitive in terms of powers. The paper concludes with an application to a real world data set, namely the earnings of the 22 highest paid participants in the inaugural season of LIV golf. [ABSTRACT FROM AUTHOR]

Wildfires pose a severe threat to the ecosystem and economy, and risk assessment is typically based on fire danger indices such as the McArthur Forest Fire Danger Index (FFDI) used in Australia. Studying the joint tail dependence structure of high-resolution spatial FFDI data is thus crucial for estimating current and future extreme wildfire risk. However, existing likelihood-based inference approaches are computationally prohibitive in high dimensions due to the need to censor observations in the bulk of the distribution. To address this, we construct models for spatial FFDI extremes by leveraging the sparse conditional independence structure of Hüsler–Reiss-type generalized Pareto processes defined on trees. These models allow for a simplified likelihood function that is computationally efficient. Our framework involves a mixture of tree-based multivariate generalized Pareto distributions with randomly generated tree structures, resulting in a flexible model that can capture nonstationary spatial dependence structures. We fit the model to summer FFDI data from different spatial clusters in Mainland Australia and 14 decadal windows between 1999 and 2022 to study local spatiotemporal variability with respect to the magnitude and extent of extreme wildfires. Our proposed method fits the margins and spatial tail dependence structure adequately and is helpful in providing extreme wildfire risk estimates. Our results identify a significant increase in spatially aggregated fire risk across a substantially large portion of Mainland Australia, which raises serious climatic concerns. Supplementary material to this paper is provided online. [ABSTRACT FROM AUTHOR]

The half-normal distribution is composited with the Pareto model to obtain a uni-parametric distribution with a heavy right tail, called the composite half-normal-Pareto distribution. This new distribution is useful for modeling positive data with atypical observations. We study the properties and the behavior of the right tail of this new distribution. We estimate the parameter using a method based on percentiles and the maximum likelihood method and assess the performance of the maximum likelihood estimator using Monte Carlo. We report three applications, one with simulated data and the others with income and expenditure data, in which the new distribution presents better performance than the Pareto distribution. [ABSTRACT FROM AUTHOR]

Multivariate extreme value distributions are a common choice for modeling multivariate extremes. In high dimensions, however, the construction of flexible and parsimonious models is challenging. We propose to combine bivariate max‐stable distributions into a Markov random field with respect to a tree. Although in general not max‐stable itself, this Markov tree is attracted by a multivariate max‐stable distribution. The latter serves as a tree‐based approximation to an unknown max‐stable distribution with the given bivariate distributions as margins. Given data, we learn an appropriate tree structure by Prim's algorithm with estimated pairwise upper tail dependence coefficients as edge weights. The distributions of pairs of connected variables can be fitted in various ways. The resulting tree‐structured max‐stable distribution allows for inference on rare event probabilities, as illustrated on river discharge data from the upper Danube basin. [ABSTRACT FROM AUTHOR]

It is well known that the increase in coastal flood hazard is expected to continue due primarily to climate change. While, previous studies have advanced probabilistic approaches for estimating future coastal flood hazard, two seminal issues have received little attention: (1) sea level trend projections that arise as a consequence of climate change not being incorporated in nonstationary coastal flood frequency analysis and (2) traditional stationary approaches that estimate return periods are not suited for analysis of nonstationary water levels. In this paper, a regression approach for sea level rise estimation is proposed to detrend water levels. The peak-over-threshold approach is used to analyze the probabilistic behavior of detrended water levels via a generalized Pareto distribution. Two interpretations of return period—the expected waiting time until an exceedance event occurs and the time associated with the expected number of exceedance events equal to one—are elaborated in a nonstationary context. By incorporating the existing sea level trend projections and using two interpretations of return period, flood hazard curves with uncertainty (i.e., water levels vs. return periods) are developed to describe the probabilistic behavior of future coastal flood hazards. Two case studies are conducted: one for Boston, Massachusetts, and one for New York City, New York. [ABSTRACT FROM AUTHOR]

Due to the continual advancements in the Internet of Things (IoT), which generate enormous volumes of data, the cloud computing infrastructure recently has received the most significance. to meet the demands made by the network of IoT devices. It is anticipated that the planned Fog computing system would constitute the next development in cloud computing. The optimal distribution of computing capacity to reduce processing times and operating costs is one of the tasks that fog computing confronts. In the IoT, fog computing is a decentralized computing approach that moves data storage and processing closer to the network's edge. This research article discusses a unique technique for lowering operating expenses and improving work scheduling in a cloud-fog environment. Non-dominated sorting genetic algorithm II (NSGA-II) is a proposal that is presented in this paper. Its purpose is to allocate service requests with the multi-objective of minimising finishing time and running cost. Determining the Pareto front that is associated with a group of perfect solutions, which are sometimes referred to as non-dominated solutions or Pareto sets, is the fundamental objective of the Pareto NSGA-II. There is a contradiction between the environmental and economic performances, which is shown by the Pareto set of suboptimal solutions that are the consequence of the bi-objective issue. [ABSTRACT FROM AUTHOR]

Motivated by empirical observations, we proposed a possible extension of Gibrat's law. By applying it into the random growth theory of income distribution, we found that the income distribution is described by a generalized Pareto distribution (GPD) with three parameters. We observed that there is a parameter η in the GPD that plays a key role in determining the shape of income distribution. By using the Kolmogorov-Smirnov test, we empirically showed that, for typical market-economy countries, η is significantly close to 0, indicating that the income distribution is characterized by a two-class pattern: The bottom 90% of the population is approximated by an exponential distribution, while the richest 1%~3% is approximated by an asymptotic power law. However, we empirically found that in China during the period of the planned economy and the early stages of market reform (from 1978 to 1990), η deviated significantly from 0, indicating that the bottom of the population no longer conformed to an exponential distribution. [ABSTRACT FROM AUTHOR]

We assume the Pareto distribution in the presence of outliers based on the Dixit model. We consider the estimation of the Bayesian Premium under squared error loss function (symmetric), linear exponential, and entropy loss functions (asymmetric), using informative and non-informative priors. We use the Lindley approximation and Markov Chain Monte Carlo methods such as the importance sampling procedure for deriving results. Finally, the results are analyzed using simulation studies. [ABSTRACT FROM AUTHOR]

Summary: Software evolution is the process of adapting, maintaining, and updating a software system. This process concentrates the most significant part of the software costs. Many works have studied software evolution and found relevant insights, such as Lehman's laws. However, there is a gap in how software systems evolve from an internal dimensions point of view. For instance, the literature has indicated how systems grow, for example, linearly, sub‐linearly, super‐linearly, or following the Pareto distribution. However, a well‐defined pattern of how this phenomenon occurs has not been established. This work aims to define a novel method to analyze and predict software evolution. We based our strategy on time series analysis, linear regression techniques, and trend tests. In this study, we applied the proposed model to investigate how the internal structure of object‐oriented software systems evolves in terms of four dimensions: coupling, inheritance hierarchy, cohesion, and class size. Applying the proposed method, we identify the functions that better explain how the analyzed dimensions evolve. Besides, we investigate how the relationship between dimension metrics behave over the systems' evolution and the set of classes existing in the systems that affect the evolution of these dimensions. We mined and analyzed data from 46 Java‐based open‐source projects. We used eight software metrics regarding the dimensions analyzed in this study. The main results of this study reveal ten software evolution properties, among them: coupling, cohesion, and inheritance evolve linearly; a relevant percentage of classes contributes to coupling and size evolution; a small percentage of classes contributes to cohesion evolution; there is no relation between the software internal dimensions' evolution. The results also indicate that our method can accurately predict how the software system will evolve in short‐term and long‐term predictions. [ABSTRACT FROM AUTHOR]

Extreme value theory plays an important role in providing approximation results for the extremes of a sequence of independent random variables when their distribution is unknown. An important one is given by the generalised Pareto distribution $H_\gamma(x)$ as an approximation of the distribution $F_t(s(t)x)$ of the excesses over a threshold t , where s (t) is a suitable norming function. We study the rate of convergence of $F_t(s(t)\cdot)$ to $H_\gamma$ in variational and Hellinger distances and translate it into that regarding the Kullback–Leibler divergence between the respective densities. [ABSTRACT FROM AUTHOR]

This paper proposes a new Topp-Leone Exponentiated Pareto (TLEtP) distribution. The new distribution family is derived by expanding the Topp Leone-G family of distributions with additional positive shape parameters. The corresponding density and distribution functions are derived and shown. Some of the derived mathematical properties of the distribution include quantile function, ordinary and incomplete moments generating function (mgf), hazard function, survival function, odd function, probability weighted moment, and distribution of order statistic. The parameters of the distribution are estimated using Maximum Likelihood method. The proposed distribution's validity is demonstrated by fitting two sets of real data and comparing the results with two existing same-family distributions, the Topp-Leone Pareto type I(TLPI) and Pareto (P), with the Akaike Information Criteria (AIC) and Bayesian Information Criteria (BIC), respectively. The comparison of the proposed Topp-Leone Exponentiated Pareto (TLEtP) to the Topp-Leone Pareto type I(TLPI) and Pareto (P) distribution demonstrate that the TLEtP distribution offers a better fit for the data sets than the other two distributions. [ABSTRACT FROM AUTHOR]

Conventional wind speed distribution methods (e.g., Rayleigh distribution and Weibull distribution) may not adequately capture complex characteristics of wind fields in mountainous areas. To address this problem, this study proposes a semi-parametric mix method for modeling the distribution of average wind speeds based on the combination of nonparametric Kernel Density Estimation (KDE) and Generalized Pareto Distribution (GPD). In the proposed method, KDE focuses on capturing the distribution in the main part of average wind speeds, while GPD aims at performing the distribution in terms of those in the extreme part. The segment point (i.e., the threshold) between KDE and GPD distributions is determined based on the combination of conditional mean excesses criterion and empirical rule. Meanwhile, the selection of modeling parameters should ensure that the mix distribution model is continuous and differentiable at the identified threshold point. Then, the commonly-used conditional probability model is further introduced to describe the wind direction distribution. Finally, a case study based on the measured 10-min average wind speeds at a mountainous bridge site is employed to demonstrate the effectiveness of the proposed method. The results indicate that: (1) the distribution of omnidirectional average wind speeds in the mountainous bridge site exhibits an obviously single-peak characteristic, while those considering wind directionality present a certain bimodal characteristic; (2) the proposed method can effectively describe wind speed distributions with different statistical characteristics, and the fitting accuracy outperforms the frequently-employed Weibull distribution model. [ABSTRACT FROM AUTHOR]

The present study aims at investigating some characterizations of a new subclass G α (μ , τ) and obtaining the bounds on the first two Taylor–Maclaurin coefficients for functions belonging to the newly introduced subclass. In order to achieve this, a compound function L x , n σ (z) is derived from the convolution of the analytic function f (z) and a modified exponential Pareto distribution G (x) in conjunction with the famous Libera integral operator L (ζ) . With the aid of the derived function, the aforementioned subclass G α (μ , τ) is introduced, while some properties of functions belonging to this subclass are considered in the open unit disk. [ABSTRACT FROM AUTHOR]

The Met Office GloSea5‐GC2 sub‐seasonal‐to‐seasonal 40‐member lagged ensemble consists of members who are up to 10 days different in age such that the between‐ensemble‐member bias is not internally consistent. Reforecasts tend to be used to convert these ensemble forecasts into anomalies from a normal state. These anomalies are however not that useful for applications where individual ensemble members are needed to drive downstream applications in the hazard and impact space. Here we explore whether there is a way of correcting for the within‐ensemble bias without using reforecasts. An investigation into the individual daily precipitation distributions from the JJAS 2019 Indian monsoon season, stratified by forecast horizon, highlights how the distribution changes, and shows that the model distribution is markedly different to the observed. Initial results suggest that it could be better to use recent model forecast distribution(s) as the reference for adjusting the model rainfall accumulations as a function of lead day horizon, that is, not attempting to correct the members to a vastly different (observed) distribution shape, but a more subtle shift towards the model's best guess of reality, rather than reality itself, to remove the between‐ensemble‐member bias. A combination of Exponential and Generalized Pareto distributions are used for parametric quantile mapping to remove this internal ensemble bias using computationally efficient pre‐computed lookup tables. Within‐ and out‐of‐sample results for the 2019 and 2020 monsoon seasons show that the method is effective in tightening precipitation gradients, with improvements in spread, accuracy and skill, especially for low accumulations. [ABSTRACT FROM AUTHOR]

A fundamental pattern in ecology is that smaller organisms are more abundant than larger organisms. This pattern is known as the individual size distribution (ISD), which is the frequency distribution of all individual body sizes in an ecosystem.The ISD is described by a power law and a major goal of size spectra analyses is to estimate the exponent of the power law, λ. However, while numerous methods have been developed to do this, they have focused almost exclusively on estimating λ from single samples.Here, we develop an extension of the truncated Pareto distribution within the probabilistic modelling language Stan. We use it to estimate multiple λs simultaneously in a hierarchical modelling approach.The most important result is the ability to examine hypotheses related to size spectra, including the assessment of fixed and random effects, within a single Bayesian generalized mixed model. While the example here uses size spectra, the technique can also be generalized to any data that follow a power law distribution. [ABSTRACT FROM AUTHOR]

The distributed training of federated machine learning, referred to as federated learning (FL), is discussed in models by multiple participants using local data without compromising data privacy and violating laws. In this paper, we consider the training of federated machine models with uncertain participation attitudes and uncertain benefits of each federated participant, and to encourage all participants to train the desired FL models, we design a fuzzy Shapley value incentive mechanism with supervision. In this incentive mechanism, if the supervision of the supervised mechanism detects that the payoffs of a federated participant reach a value that satisfies the Pareto optimality condition, the federated participant receives a distribution of federated payoffs. The results of numerical experiments demonstrate that the mechanism successfully achieves a fair and Pareto optimal distribution of payoffs. The contradiction between fairness and Pareto-efficient optimization is solved by introducing a supervised mechanism. [ABSTRACT FROM AUTHOR]

Clustered bivariate survival data arise in various fields, such as biology and medicine, when individuals in a dataset are clustered and exhibit two survival outcomes. Recently, the joint frailty-copula model was proposed to analyze clustered bivariate survival outcomes by accommodating the between-cluster heterogeneity via a shared frailty term. In this model, researchers fitted the baseline hazard functions via the nonparametric model, the spline model, or the Weibull model. However, when a population has extremely large survival time, the baseline hazard functions are better modeled by a heavy-tailed distribution. In this paper, we adopt the Pareto type I distribution for the joint frailty-copula model, which is one of the most popular heavy-tailed distributions. We show that the moments of the Pareto type I joint frailty copula model diverge to infinity owing to the heavy right-tail. We develop statistical inference methods based on three types of censoring schemes: (i) bivariate random censoring, (ii) semi-competing risks, and (iii) competing risks. We develop maximum likelihood estimation procedures, and make our computational tools available for users. Simulations are performed to check the accuracy of the proposed method. We finally analyze a real dataset for illustration. [ABSTRACT FROM AUTHOR]

Droughts are catastrophic and have become frequent in the last decade. The Upper Kangsabati River Basin (UKRB) in West Bengal state of India is affected by droughts. This research comprehensively evaluates meteorological drought and its spatial variability within the basin. Drought severity levels vary spatially with time, making it difficult for policymakers to prioritize preventive measures for different parts of the UKRB. Droughts were characterized using Standardized Precipitation Index (SPI) for 16 precipitation grid points. SPI-12 showed that the basin experienced two severe and three extreme drought years within the study period. Run theory was applied on SPI-3 to extract drought events, which varied from 34 to 41, spatially in the basin, with the maximum severity being 18.08. After fitting the appropriate marginal distributions to the extracted drought duration and severity, their bivariate relationship was established using copula. Generalized Pareto distribution and Frank copula fitted best for the marginal and bivariate distributions, respectively. Finally, the conditional OR return period of the historical droughts was determined from that relationship. It showed that parts of the basin experienced extreme drought of 50-year return period. The most likely event scenario was determined from the OR return period contours and applied to create the spatially distributed drought hazard maps, which is the uniqueness of the study. The present study suggested that the western and central regions of UKRB would experience more severe droughts when return period increases. Additionally, the modified Mann–Kendall (MMK) test applied to detect drought trends indicated no significant trend for monsoon months. [ABSTRACT FROM AUTHOR]

The west side of the Antarctic Peninsula (AP) has shown great variability since the middle of the last century characterized by warming mainly because of the oceanic and atmospheric effects such as the disintegration of floating ice and the strength of westerly winds. Here, we used two climatic databases (reanalysis from 1979 to 2020 and surface stations from 1947 to 2020) to investigate trends in extreme air temperatures and wind components in the oceanic region between 55° S and 70° S in the west (75° W) and in the east sector (45° W) and over the AP (60° W). Non-parametric statistical trend tests and extreme value approaches are used. A set of annual, monthly, and seasonal series are fitted. The extremal index is applied to measure the degree of independence of monthly excesses over a threshold considered extreme events. Increasing trends are verified in the annual and monthly temperature and wind series. The greatest trends are observed for seasonal series from reanalysis without change-point in summer and winter. Decreasing trends are observed for maximum temperature in summer and positive trends mainly for the westerly winds over the AP. But in winter, the maximum temperature shows an increasing trend also over the AP. Most of reanalysis seasonal minimum temperature and wind components as well as maximum and minimum temperatures from stations present increasing trends with change-point but tend to stability after the breakpoints. The generalized distribution (GEV) is used to fit temperatures and westerly wind between South America (SA) and north of the AP. The 100-year return levels exceed the maximum value of the maximum temperature in Esperanza and maximum westerly winds at several grid points. Pareto and Poison distributions are applied for the maximum temperatures from stations and the 100-year return levels are not exceeded. Our findings show significant positive trends for monthly wind components near the SA in the region of the westerly winds whose changes in position influence directly the SAM, which modifies the atmospheric patterns in the South Hemisphere (SH). A predominance of seasonal warming is identified, which may impact the climate with consequences not only locally but also in other regions. [ABSTRACT FROM AUTHOR]

In statistical modeling, lifetime datasets play an important and significant role. Weighted distributions can be useful to attain the essential purposes relating to the developed distributions' flexibility and to improve further compliances in data forming; they provide the extension of distributions. The current study suggests a new best-fit probability distribution model based on Pareto distribution. The new model is called Survival Weighted Pareto (SWP) distribution model. Furthermore, the statistical expressions for different properties, which include moments, inverse moments, quantile function, and order statistics, are reported. Moreover, to check the performance and the behavior of different estimators using different sample sizes, a simulation study, which is based on SWP distribution, is performed. According to the simulation results, it is established that the proposed model is a most useful fitted probability model. In addition, an application of the SWP model for three datasets is provided to check the goodness of fit measures of the model. [ABSTRACT FROM AUTHOR]

We consider a constructive definition of the multivariate Pareto that factorizes the random vector into a radial component and an independent angular component. The former follows a univariate Pareto distribution, and the latter is defined on the surface of the positive orthant of the infinity norm unit hypercube. We propose a method for inferring the distribution of the angular component by identifying its support as the limit of the positive orthant of the unit p-norm spheres and introduce a projected gamma family of distributions defined through the normalization of a vector of independent random gammas to the space. This serves to construct a flexible family of distributions obtained as a Dirichlet process mixture of projected gammas. For model assessment, we discuss scoring methods appropriate to distributions on the unit hypercube. In particular, working with the energy score criterion, we develop a kernel metric that produces a proper scoring rule and presents a simulation study to compare different modeling choices using the proposed metric. Using our approach, we describe the dependence structure of extreme values in the integrated vapor transport (IVT), data describing the flow of atmospheric moisture along the coast of California. We find clear but heterogeneous geographical dependence. [ABSTRACT FROM AUTHOR]

We develop a game theoretic model to study the compatibility and distribution decisions of two asymmetric competing platform owners. It is found that there are two equilibrium distribution structures for the two platform firms. Then a Pareto optimality distribution structure for the two firms is discovered. We proceed to discuss the platform's compatibility decision under the equilibrium distribution structures, and find that the equilibrium compatibility decisions depend on the average royalty. We further examine the impact of firm's distribution decisions over their compatibility decisions. Finally, we discuss how retailers will benefit from platform owner's compatibility decisions. [ABSTRACT FROM AUTHOR]

Context. Analysis of data uncertainties in modeling and forecasting of actuarial processes is very important issue because it allows actuaries to efficiently construct mathematical models and minimize insurance risks considering different situations. Objective. The goal of the following research is to develop an approach that allows for predicting future insurance payments with prior minimization of possible statistical data uncertainty. Method. The proposed method allows for the implementation of algorithms for estimating the parameters of generalized linear models with the preliminary application to data of the optimal Kalman filter. The results demonstrated better forecast results and more adequate model structures. This approach was applied successfully to the simulation procedure of insurance data. For generating insurance dataset the next features of clients were used: age; sex; body mass index (applying normal distribution); number of children (between 0 and 5); smoker status; region (north, east, south, west, center); charges. For creating the last feature normal distribution with known variance and a logarithmic function, exponential distribution with the identity link function and Pareto distribution with a known scale parameter and a negative linear function were used. Results. The proposed approach was implemented in the form of information processing system for solving the problem of predicting insurance payments based on insurance data and with taking into account the noise of the data. Conclusions. The conducted experiments confirmed that the proposed approach allows for more adequate model constructing and accurate forecasting of insurance payments, which is important point in the analysis of actuarial risks. The prospects for further research may include the use of this approach proposed in other fields of insurance related to availability of actuarial risk. A specialized intellectual decision support system should be designed and implemented to solve the problem by using actual insurance data from real world in online mode as well as modern information technologies and intellectual data analysis. [ABSTRACT FROM AUTHOR]

The electric power infrastructure is the cornerstone of contemporary society's sustenance and advancement. Within the intelligent electric power financial system, substantial inefficiency and waste in information management persist, leading to an escalating depletion of resources. Addressing diverse objectives encompassing economic, environmental, and societal concerns within the power system helps the study to undertake a comprehensive, integrated optimal design and operational scheduling based on a multiobjective optimization algorithm. This article centers on optimizing the power financial system by considering fuel cost, active network loss, and voltage quality as primary objectives. A mathematical model encapsulates these objectives, integrating equations and inequality constraints and subsequently introducing enhancements to the differential evolutionary algorithm. Adaptive variation and dynamic crossover factors within crossover, variation, and selection operations are integrated to optimize algorithm parameters, specifically catering to the multiobjective optimization of the electric power system. An adaptive grid method and cyclic crowding degree ensure population diversity and control the Pareto front distribution. They experimentally validated the approach and the comparisons conducted against AG-MOPSO, INSGA-II, and NSDE algorithms across standard test functions: ZDT1, ZDT2, ZDT3, and DTLZ4. The convergence evaluation indices for this study's scheme on ZDT1 and ZDT2 are 0.000938 and 0.0034, respectively. Additionally, distribution evaluation indices on ZDT1, ZDT2, ZDT3, and ZDT4 stand at 0.0018, 0.0026, 0.0027, and 0.0009, respectively. These indices indicate a robust convergence and distribution, facilitating the optimization of electric power financial information management and the intelligent handling of the electric power financial system's information, thereby enhancing the allocation of material and financial resources. [ABSTRACT FROM AUTHOR]