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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

A new proportional stochastic order is defined based on the concept of quantile residual life. In addition, a new aging class of life distributions, namely, decreasing proportional failure rate distributions, was defined. Moreover, two other aging classes based on the proposed stochastic ordering are defined and investigated: decreasing proportional α-quantile residual life and its dual increasing proportional α-quantile residual life. The relationship between the proportional failure rate and proportional α-quantile residual life has been discussed. Some well-known and useful models are classified in terms of the proportional α-quantile residual life function. Finally, a new modified Pareto distribution with a decreasing proportional failure rate and an increasing proportional α-quantile residual life function was presented and studied.

In this paper, we compared the Exact Bahadur Slope (EBS) and the asymptotic relative efficiency of four combination methods for testing a single hypothesis against a one-sided alternative in the case of Pareto distribution when the number of tests tends to infinity. These methods combine the p-value of the corresponding test into one overall test. Fisher's, logistic, the sum of p-values, and inverse normal procedures are the four techniques used in our study. To study the performance of the combination methods, we derived the EBS expressions and compared the limit ratios locally and for large values of the shape parameter of the Pareto distribution via EBS. We also computed the EBS numerically for when the parameter of interest starts moving from the null space and applied the four methods to real data examples. We found that Fisher's method uniformly dominates the other methods in terms of EBS.

Abstract The Pareto distribution is of paramount importance in actuarial science, wealth distribution, finance, etc. This paper introduces a control chart inspired by Shewhart's methodology, designed for monitoring shifts in the Pareto distribution through a repetitive sampling approach. The chart employs a modified statistic that combines shape and threshold parameters as its plotting statistic. Coefficients for the Shewhart-type Pareto chart are computed for two-phase limits. The performance of the suggested chart is assessed in terms of run length characteristics, assuming a shift in the process mean. Additionally, we conduct an efficiency comparison with existing control charts. The findings suggest that, on average, the proposed Pareto chart demonstrates greater efficiency in promptly detecting changes compared to alternative methods. To illustrate the practical application of our approach, we present an example using revenue data.

This paper proposes an inference approach based on a pivotal quantity under the adaptive progressive Type-II censoring scheme. To exemplify the proposed methodology, an extensively employed distribution, a Pareto distribution, is utilized. This distribution has limitations in estimating confidence intervals for unknown parameters from classical methods such as the maximum likelihood and bootstrap methods. For example, in the maximum likelihood method, the asymptotic variance-covariance matrix does not always exist. In addition, both classical methods can yield confidence intervals that do not satisfy nominal levels when a sample size is not large enough. Our approach resolves these limitations by allowing us to construct exact intervals for unknown parameters with computational simplicity. Aside from this, the proposed approach leads to closed-form estimators with properties such as unbiasedness and consistency. To verify the validity of the proposed methodology, two approaches, a Monte Carlo simulation and a real-world data analysis, are conducted. The simulation testifies to the superior performance of the proposed methodology as compared to the maximum likelihood method, and the real-world data analysis examines the applicability and scalability of the proposed methodology.

According to earlier research, transmuting a standard distribution often results in a compound distribution that performs better and is more flexible. In light of this fact, this article proposes two novel generalized versions of the exponentiated Pareto-I distribution, called cubic transmuted exponentiated Pareto-I and fourth rank transmuted exponentiated Pareto-I by using the generalization formula for transmuted distribution. Some statistical properties are derived. Model parameters are estimated using the maximum likelihood method. Finally, an application of the two proposed distributions to two real data sets with diverse shapes is illustrated and compared with some distributions based on the exponential family and the exponentiated Pareto-I distribution. The applications suggest that the fourth version performs better than the cubic one for all shapes of the distribution. The new exponentiated Pareto-I models exhibit constant, upside-down, and bathtub hazard rates. The justification for the practicality of the new lifetime models is based on their ability to model real-life data sets from different perspectives.

Generalized Pareto distribution (GPD), an asymmetrical distribution, primarily models exceedances over a high threshold in many applications. Within the peaks-over-threshold (POT) framework, we consider a new GPD parameter estimation method to estimate a common tail risk measure, the value at risk (VaR). The proposed method is more suitable for the POT framework and makes full use of data information. Specifically, our estimation method builds upon the generalized probability weighted moments method and integrates it with the nonlinear weighted least squares method. We use exceedances for the GPD, minimizing the sum of squared differences between the sample and population moments of a function of GPD random variables. At the same time, the proposed estimator uses three iterations and assigns weight to further improving the estimated performance. Under Monte Carlo simulations and with a real heavy-tailed dataset, the simulation results show the advantage of the newly proposed estimator, particularly when VaRs are at high confidence levels. In addition, by simulating other heavy-tailed distributions, our method still exhibits good performance in estimating misjudgment distributions. [ABSTRACT FROM AUTHOR]

Progressive type-II (Prog-II) censoring schemes are gaining traction in estimating the parameters, and reliability characteristics of lifetime distributions. The focus of this paper is to enhance the accuracy and reliability of such estimations for the inverse power exponentiated Pareto (IPEP) distribution, a flexible extension of the exponentiated Pareto distribution suitable for modeling engineering and medical data. We aim to develop novel statistical inference methods applicable under Prog-II censoring, leading to a deeper understanding of failure time behavior, improved decision-making, and enhanced overall model reliability. Our investigation employs both classical and Bayesian approaches. The classical technique involves constructing maximum likelihood estimators of the model parameters and their bootstrap covariance intervals. Using the Gibbs process constructed by the Metropolis–Hasting sampler technique, the Markov chain Monte Carlo method provides Bayesian estimates of the unknown parameters. In addition, an actual data analysis is carried out to examine the estimation process's performance under this ideal scheme. [ABSTRACT FROM AUTHOR]

As the most commonly used attack strategy by Botnets, the Domain Generation Algorithm (DGA) has strong invisibility and variability. Using deep learning models to detect different families of DGA domain names can improve the network defense ability against hackers. However, this task faces an extremely imbalanced sample size among different DGA categories, which leads to low classification accuracy for small sample categories and even classification failure for some categories. To address this issue, we introduce the long-tailed concept and augment the data of small sample categories by transferring pre-trained knowledge. Firstly, we propose the Data Balanced Review Method (DBRM) to reduce the sample size difference between the categories, thus a relatively balanced dataset for transfer learning is generated. Secondly, we propose the Knowledge Transfer Model (KTM) to enhance the knowledge of the small sample categories. KTM uses a multi-stage transfer to transfer weights from the big sample categories to the small sample categories. Furthermore, we propose the Knowledge Distillation Transfer Model (KDTM) to relieve the catastrophic forgetting problem caused by transfer learning, which adds knowledge distillation loss based on the KTM. The experimental results show that KDTM can significantly improve the classification performance of all categories, especially the small sample categories. It can achieve a state-of-the-art macro average F1 score of 84.5%. The robustness of the KDTM model is verified using three DGA datasets that follow the Pareto distributions. [ABSTRACT FROM AUTHOR]

We explore formal similarities and mathematical transformation formulas between general trace-form entropies and the Gini index, originally used in quantifying income and wealth inequalities. We utilize the notion of gintropy introduced in our earlier works as a certain property of the Lorenz curve drawn in the map of the tail-integrated cumulative population and wealth fractions. In particular, we rediscover Tsallis' q-entropy formula related to the Pareto distribution. As a novel result, we express the traditional entropy in terms of gintropy and reconstruct further non-additive formulas. A dynamical model calculation of the evolution of Gini index is also presented. [ABSTRACT FROM AUTHOR]

The detection of nonstationarities in partial duration time series (PDS) depends on several factors, including the length of the time series, the selected statistical test, and the heaviness of the tail of the distribution. Because of the more limited attention received in the literature when compared to the trend detection on block maxima variables, we perform a Monte Carlo simulation study to evaluate the performance of different approaches: Spearman's rho, Mann–Kendall, ordinary least squares (OLS), Sen's slope estimator (SEN), and the nonstationary generalized Pareto distribution fit to identify the presence of trends in PDS records characterized by different sample sizes (n), shape parameter (ξ) and degrees of nonstationarity. The results point to a power gain for all tests by increasing n and the degree of nonstationarity and by reducing ξ. The use of a nonparametric test is recommended in samples with a high positive skew. Furthermore, the use of sampling rates greater than one to increase the PDS sample size is encouraged, especially when dealing with small records. The use of SEN to estimate the magnitude of a trend is preferable over OLS due to its slightly smaller probability of occurrence of type S error when ξ is positive. [ABSTRACT FROM AUTHOR]

This paper proposes an inference approach based on a pivotal quantity under the adaptive progressive Type-II censoring scheme. To exemplify the proposed methodology, an extensively employed distribution, a Pareto distribution, is utilized. This distribution has limitations in estimating confidence intervals for unknown parameters from classical methods such as the maximum likelihood and bootstrap methods. For example, in the maximum likelihood method, the asymptotic variance-covariance matrix does not always exist. In addition, both classical methods can yield confidence intervals that do not satisfy nominal levels when a sample size is not large enough. Our approach resolves these limitations by allowing us to construct exact intervals for unknown parameters with computational simplicity. Aside from this, the proposed approach leads to closed-form estimators with properties such as unbiasedness and consistency. To verify the validity of the proposed methodology, two approaches, a Monte Carlo simulation and a real-world data analysis, are conducted. The simulation testifies to the superior performance of the proposed methodology as compared to the maximum likelihood method, and the real-world data analysis examines the applicability and scalability of the proposed methodology. [ABSTRACT FROM AUTHOR]

Numerous robust estimators exist as alternatives to the maximum likelihood estimator (MLE) when a completely observed ground-up loss severity sample dataset is available. However, the options for robust alternatives to a MLE become significantly limited when dealing with grouped loss severity data, with only a handful of methods, like least squares, minimum Hellinger distance, and optimal bounded influence function, available. This paper introduces a novel robust estimation technique, the Method of Truncated Moments (MTuM), pecifically designed to estimate the tail index of a Pareto distribution from grouped data. Inferential justification of the MTuM is established by employing the central limit theorem and validating it through a comprehensive simulation study. [ABSTRACT FROM AUTHOR]

A theoretical foundation for predicting the distribution of trade strength and the rate of change of trade strength was developed. These two quantities were found to satisfy the Pareto distribution function. The equations were confirmed using data from the World Integrated Trade Solution and the World Bank by comparing the Akaike information criterion and Bayesian information criterion to five types of distribution functions (exponential, lognormal, gamma, Pareto, and Weibull). Furthermore, the fitted Pareto power parameter is quite similar to the theoretical prediction. The developed distribution function is expected to be useful in forecasting international trade in countries and global economics, enabling the implementation of optimal policies. [ABSTRACT FROM AUTHOR]

The Pareto distribution is of paramount importance in actuarial science, wealth distribution, finance, etc. This paper introduces a control chart inspired by Shewhart's methodology, designed for monitoring shifts in the Pareto distribution through a repetitive sampling approach. The chart employs a modified statistic that combines shape and threshold parameters as its plotting statistic. Coefficients for the Shewhart-type Pareto chart are computed for two-phase limits. The performance of the suggested chart is assessed in terms of run length characteristics, assuming a shift in the process mean. Additionally, we conduct an efficiency comparison with existing control charts. The findings suggest that, on average, the proposed Pareto chart demonstrates greater efficiency in promptly detecting changes compared to alternative methods. To illustrate the practical application of our approach, we present an example using revenue data. [ABSTRACT FROM AUTHOR]

It has been known for a long time that (1) when graphs of income amount on income relative rank for two income distributions intersect twice, three "transfer groups" are generated, with the poorest and richest both gaining under the same alternative income distribution and the middle group losing; and (2) the linear income tax system satisfies three fundamental principles of tax justice, namely, that as pretax income increases, three quantities should also increase--posttax income, tax amount, and tax rate. This paper links those two ideas, suggesting that the linear income tax system may be the natural and most effective way to guard against poverty reduction policies which, while helping the poorest, as urged by Rawls, may harm the middle, contributing to the weakening of the middle class, thought at least since Aristotle to be the backbone of society. This paper illustrates the two approaches with one initial distribution and three alternative final distributions, contrasting their minimum, median, proportion below the mean, and inequality. It also shows how to guard the linear income tax system against violating the tax amount principle of tax fairness when there is an injection of resources (e.g., from deficit spending or oil revenues) and how to empirically estimate the parameters (e.g., the marginal tax rate) of the linear income system that the population will regard as fair. [ABSTRACT FROM AUTHOR]

Extreme rainfall events in the Chi watershed of northeastern Thailand have significant implications for the safe and economic design of engineered structures and effective reservoir management. This study investigates the characteristics of extreme rainfall events in the watershed and their implications for flood risk management. We apply extreme value theory to historical maximum cumulative rainfall data for consecutive rainy days from 1984 to 2022. The generalized Pareto distribution (GPD) was used to model the extreme rainfall data, with the parameters estimated using maximum likelihood estimation (MLE) and linear moment estimation (L-ME) methods based on specific conditions. The goodness-of-fit tests confirm the suitability of the GPD for the data, with p values exceeding 0.05. Our findings reveal that certain regions, notably Udon Thani, Chaiyaphum, Maha Sarakham, Tha Phra Agromet., Roi Et, and Sisaket provinces, show the highest return levels for consecutive 2 d (CONS-2) and 3 d (CONS-3) rainfall. These results underscore the heightened risk of flash flooding in these regions, even with short periods of continuous rainfall. Based on our findings, we developed 2D return level maps using the Q-geographic information system (Q-GIS) program, providing a visual tool to assist with flood risk management. The study offers valuable insights for designing effective flood management strategies and highlights the need for considering extreme rainfall events in water management and planning. Future research could extend our findings through spatial correlation analysis and the use of copula functions. Overall, this study emphasizes the importance of preparing for extreme rainfall events, particularly in the era of climate change, to mitigate potential flood-related damage. [ABSTRACT FROM AUTHOR]

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

In the context of robust Bayesian analysis, studies mainly focus on computing the range of some quantities of interest when the prior distribution varies in a class. We use the concept of distorted bands to introduce a family of priors on the shape parameter of the Generalized Pareto distribution. We show how certain properties of the likelihood ratio order allow us to propose novel sensitivity measures for Value at Risk and Conditional Value at Risk, which are the most useful and reliable risk measures. Although we focus on the Generalized Pareto distribution, which is essential in Extreme Value Theory, the new sensitivity measures could be employed for all the distributions that verify certain conditions related to likelihood ratio order. A thorough simulation study was carried out to perform a sensitivity analysis, and two illustrative examples are also provided. [ABSTRACT FROM AUTHOR]

Estimating generalised Pareto distribution (GPD) parameters is a fundamental step in modelling the extremevalue distribution of random variables. It is generally done with the maximum likelihood method, but there are generally difficulties in estimating GPD parameters using this method as there is no closed-form solution for the first derivative of the GPD log-likelihood function. This makes the solution difficult to determine analytically. However, numerical methods can be used as an alternative. Therefore, this study estimates the solution numerically using a simple fixed-point iteration method that is intuitive for both practitioners and professionals. We obtained three fixed-point iterations when estimating GPD parameters that met the unbiased estimator and convergence criteria. The iterations allow practitioners and professionals to directly and efficiently estimate GPD parameters when modelling extreme-value distributions of random variables. [ABSTRACT FROM AUTHOR]

Intensity‐Duration‐Area‐Frequency (IDAF) models provide the mathematical link between precipitation intensities (I), durations (D), areas (A), and frequency of occurrence (F). They play a critical role in hydrological design, areal rainfall hazard quantification, storm characterization, and early warning system development. IDAF models extend the conventional Intensity‐Duration‐Frequency models by accounting for the spatial extent of precipitation (i.e., the area). In this study, we develop IDAF models using the entire non‐zero precipitation intensities, not only the extremes. We use the extended generalized Pareto distribution (EGPD) to model the precipitation intensities. To build the IDAF models, we adopt a data‐driven approach that allows the linkage of EGPD parameters with duration and area, based on empirically determined parametric relationships. The inference of model parameters is done using a global maximum likelihood estimation, and uncertainties are assessed by the bootstrap method. The study area is Switzerland, a topographically complex region of 42,000 km2 with regional precipitation variability and clear seasonality. The study utilizes 17 years of data from CombiPrecip, a radar‐reanalysis product developed by geostatistically merging radar and rain gauge data in an operational setting. We build the IDAF models for the spatiotemporal range of 1–72 hr and 1 to 1,089 km2 at each pixel in the study area. To the best of our knowledge, our study is the first attempt to use the EGPD in IDAF curve modeling. It discusses the use and limitations of CombiPrecip in extreme value analysis and highlights the challenges of modeling areal precipitation in a complex topographical environment. Key Points: We develop seasonal Intensity Duration Area Frequency models at every pixel location in SwitzerlandWe use all the non‐zero precipitation data and model the intensities using the extended generalized Pareto distributionWe highlight the complexity of modeling areal precipitation in mountainous regions [ABSTRACT FROM AUTHOR]

The Pareto distribution plays an important role in many data analysis tasks. An important aspect of this distribution is the estimation of its parameters. Several studies use classical methods, Bayes, and the neural network (NN) to evaluate Pareto parameters. Others have attempted to combine classical methods with a single NN-based. However, there isn't enough research to determine the sensitivity of the single NN to the specifics of the training data due to its stochastic training algorithm in the parameter estimation field. The current research aims to prove the efficiency of the aggregation of weighted multiple NN models and weighted ordinary least-squares regression algorithm to overcome the specifics of the training data and the sensitivity to outliers, respectively. The proposed method enables a locally less accurate model to participate to a lesser extent in the overall aggregation. The proposed method was compared with prevalent methods in the area, including the ordinary least squares, weighted ordinary least squares, maximum likelihood estimation, and the Bayes' using Monte Carlo simulations. The results verified the superiority of the proposed method in terms of regression error metrics. Moreover, it can be adapted to a variety of distributions. [ABSTRACT FROM AUTHOR]

The main goal of this article is to determine the optimally weighted coefficients (Ω 1 and Ω 2) of the balanced loss function of the form. L Κ , Ω , ξ o Ψ (σ) , ξ = Ω 1 γ σ Κ ξ o , ξ + Ω 2 γ σ Κ Ψ (σ) , ξ ; Ω 1 + Ω 2 = 1. Based on Type II Censored Data, by applying non-linear programming to estimate the shape parameter and some survival time characteristics, such as reliability and hazard functions of the Pareto distribution. Considering two balanced loss functions (BLF), including balanced square error loss function (BSELF) and balanced linear exponential loss function (BLLF), the calculation is based on the balanced loss function, including symmetric and asymmetric loss functions, as a special case. Use Monte Carlo simulation to pass Bayesian and maximum likelihood estimators through. The results of the simulation showed that the proposed model BLLF has the best performance. Moreover, the simulation verified that the balanced loss functions are always better than the corresponding loss function. [ABSTRACT FROM AUTHOR]

Depth regulates many attributes of aquatic ecosystems, but relatively few lakes are measured, and existing datasets are biased toward large lakes. To address this, we used a large dataset of maximum (Zmax; n = 16,831) and mean (Zmean; n = 5,881) depth observations to create new depth models, focusing on lakes < 1,000 ha. We then used the models to characterize patterns in lake basin shape and volume. We included terrain metrics, water temperature and reflectance, polygon attributes, and other predictors in a random forest model. Our final models generally outperformed existing models (ZmaxR2=0.35; root mean square error [RMSE] = 8.0 m and ZmeanR2=0.36; RMSE = 3.0 m). Our models show that lake depth followed a Pareto distribution, with 2.8 orders of magnitude fewer lakes for an order of magnitude increase in depth. In addition, despite orders of magnitude variation in surface area, most size classes had a modal maximum depth of ~ 5 m. Concave (bowl‐shaped) lake basins represented 79% of all lakes, but lakes were more convex (funnel‐shaped) as surface area increased. Across the conterminous United States, 9.8% of all lake water was within the top meter of the water column, and 48% in the top 10 m. Excluding the Laurentian Great Lakes, we estimate the total volume in the conterminous United States is 1,057–1,294 km3, depending on whether Zmax or Zmean was modeled. Lake volume also exhibited substantial geographic variation, with high volumes in the upper Midwest, Northeast, and Florida and low volumes in the southwestern United States. [ABSTRACT FROM AUTHOR]

The drill pipe of a rotary rig is subject to the dynamic influence of non-stationary loads, including rotation torque and applied force. In order to address the challenge of simultaneously extrapolating multiple non-stationary loads, a novel extrapolation framework is proposed. This framework utilizes rainflow counting to obtain mean and amplitude sequences of the loads. The extreme values of the amplitude sequence are fitted using the Generalized Pareto Distribution (GPD), while the median values are fitted using the Double Kernel Density Estimation (DKDE). By extrapolating the Inverse Cumulative Distribution Function (ICDF) based on the fitted distribution, a new amplitude sequence can be derived. The combination of this extrapolated amplitude sequence with the original mean sequence forms a new load spectrum. The results of applying the proposed extrapolation method to the drill pipe of a rotary rig demonstrate the ability of the method to yield conservative extrapolation results and accurately capture the variations in damage under the original working conditions. [ABSTRACT FROM AUTHOR]

We study the effect of interest rates on wealth inequality. While lower rates decrease the growth rate of rentiers, they also increase the growth rate of entrepreneurs by making it cheaper to raise capital. To understand which effect dominates, we derive a sufficient statistic for the effect of interest rates on the Pareto exponent of the wealth distribution: it depends on the lifetime equity and debt issuance rate of individuals in the right tail of the wealth distribution. We estimate this sufficient statistic using new data on the trajectory of top fortunes in the U.S. Overall, we find that the secular decline in interest rates (or more generally of required rates of returns) can account for about 40% of the rise in Pareto inequality; that is, the degree to which the super rich pulled ahead relative to the rich. [ABSTRACT FROM AUTHOR]

Threshold selection is challenging when analyzing tail data with a generalized Pareto distribution. Data below the threshold was not used in the model, resulting in incomplete characterization of the whole data. This paper applied the Gamma distribution, Weibull distribution, and lognormal distribution to fit the central data separately, and a generalized Pareto distribution (GPD) was used to analyze the tail data. In such composite models, the thresholds are estimated directly as parameters. We proposed an empirical distribution function-based parameter estimation method. The absolute value of the difference between the empirical distribution function and the composite distribution function was used as a loss function to obtain an estimate of the parameter. This parameter estimation method is suitable for complex multiparameter distributions. The estimation method based on the empirical distribution function was verified to be feasible through simulation studies. The composite model and the estimation method based on the empirical distribution function were applied to study the earthquake magnitude data to provide a reference for earthquake hazard analysis. [ABSTRACT FROM AUTHOR]

Abstract Background Within the Hymenoptera, bees are notable for their relationship with flowering plants, being almost entirely dependent on plant pollen and nectar. Though functionally herbivorous, as a result of their role as pollinators, bees have received comparatively little attention as models for insect herbivory. Bees often display dietary specialization, but quantitative comparison against other herbivorous insects has not previously been conducted. Results In the most comprehensive analysis to date for 860 bee species, dietary specialization amounted to 50.1% of studied species collecting pollen from between 1 and 2 botanical families with a relatively long tail of dietary generalists, with 11.1% of species collecting from more than 10 botanical families. This distribution deviated from the truncated Pareto distribution of dietary breadth seen in other herbivorous insect lineages. However, this deviation was predominantly due to eusocial bee lineages, which show a range of dietary breadths that conformed to a normal distribution, while solitary bees show a typical truncated distribution not strongly different from other herbivorous insects. We hypothesize that the relatively low level of dietary specialization in bees as a whole reflects the relaxation of the constraints typically observed in herbivorous insects with a comparatively reduced importance of plant chemistry and comparatively increased importance of phenology and foraging efficiency. The long flight periods of eusocial bees that are necessary to allow overlapping generations both allows and necessitates the use of multiple flowering resources, whereas solitary bees with short flight periods have more limited access to varied resources within a constrained activity period. Conclusions Collectively, solitary bees show slightly lower specialization compared to other herbivorous insects, possibly due to their balanced relationship with plants, rather than direct antagonism such as seen in the direct consumption of plant tissues. An additional factor may be the mediocre diversity of bees at low latitudes combined with low levels of dietary specialization, whereas these areas typically display a high rate of specialization by herbivorous insects in general. Though the most important factors structuring dietary specialization in bees appear to differ from many other herbivorous insects, solitary bees show a surprisingly similar overall pattern of dietary specialization.