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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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

The Central Limit Theorem justifies using a normal distribution when looking at sums of many terms. In a parallel way, extreme value distributions arise in the study of maxima of many terms. The goal of this paper is to briefly review the univariate theory of extremes based on the Fisher-Tippet-Gnedenko Theorem. We then state the basics of the multivariate theory, which is significantly more complicated because it requires a measure to define the distribution. Some properties of these laws are explored, including a description of the support, an expression for the density when it exists, and some examples that illustrate possible joint dependence structures. [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]

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]

There are many real-life situations, where data require probability distribution function which have decreasing or upside-down bathtub (UBT) shaped failure rate function. The inverse power burr hatke distribution consists both decreasing and UBT shaped failure rate functions. Here, we address the different estimation methods of the parameter and reliability characteristics of the inverse Pareto distribution from both classical and Bayesian approaches. We consider classical estimation procedures to estimate the unknown parameter of inverse power burr-hatke distribution, such as maximum likelihood. Also, we consider Bayesian estimation using squared error loss function based joint priors. The Monte Carlo simulations are performed to compare the performances of the obtained estimators in mean square error sense. Finally, the flexibility of the proposed distribution is illustrated empirically using one real-life datasets. The analyzed data shows that the introduced distribution provides a superior fit than some important competing distributions such as the Weibull, inverse Pareto and Burr-Hatke 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]

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]

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]

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]

In recent years, several probability distributions have been introduced in the literature to analyze the data exhibiting an upside-down bathtub–shaped failure rate; an inverse Pareto distribution (IPD) is an appropriate choice among them. For stress–strength reliability models, estimation of parameters is an interesting area of research. In this article, we estimate the stress–strength reliability parameter R = P (X > Y) (where X and Y are strength and stress variables, respectively) of the IPD, whereby we focus on the problem of fixed-accuracy confidence interval estimation of R. It is established that the proposed interval estimation problem cannot be solved with the help of any fixed sample technique. As a result, we propose a two-stage sequential sampling strategy (which reduces the sample size significantly) to solve the given estimation problem. We obtain the expressions of several exact operating characteristics associated with our two-stage sampling technique. We also establish that the proposed two-stage procedure enjoys interesting first-order asymptotic properties. The detailed simulation analyses support our theoretical findings, and two real data sets based on insurance claims reinforce the practical utility of the proposed technique. [ABSTRACT FROM AUTHOR]

Classical survival models assume homogeneity among the population of individuals who are susceptible to the event of interest. However, in many practical circumstances, there is a certain amount of unobserved heterogeneity that can be caused by a variety of sources, such as environmental or genetic factors. If the heterogeneity is ignored, many issues could arise, including an overestimation of the hazard rate and inaccurate estimates of the regression coefficients. Frailty models are usually used to model the heterogeneity among individuals. In this paper, we propose a novel univariate frailty model. The frailty variable is assumed to follow the Two Parameter Lindley distribution. The maximum likelihood method is used to estimate the model parameters. The baseline hazard functions are assumed to follow Weibull, Exponential, Gompertz, and Pareto distributions, and a simulation study is performed under this assumption. We examine the characteristics of the distribution and assess its performance compared to other distributions that are frequently applied in frailty modeling by using both Nikulin-Rao-Robson and Bagdonavicius-Nikulin goodness-of-fit tests to determine the adequacy of the model. We analyze a fresh medical dataset collected from an emergency hospital in Algeria to evaluate the effectiveness and applicability of the proposed model. [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]

In many practical situations, we observe a special Burr probability distribution — e.g., Burr distribution describes the distribution of people by income, it describes the rainfall data, etc. In this paper, we provide a theoretical explanation for the ubiquity of Burr distributions: namely, we show that this distribution naturally follows from scale-invariance. To be more precise, the simplest distribution that can be obtained from scale invariance is the Pareto distribution — a frequent particular case of the general Burr family of distributions. Next simplest are all distributions from the Burr family. We also use the scale-invariance approach to come up with a more general class of distributions that will, hopefully, provide an even more accurate description of the corresponding phenomena. [ABSTRACT FROM AUTHOR]

The downside risks in stock markets may lead to huge losses and bring profound impact on businesses and governments. In order to model and predict these risks in Chinese stock markets, we propose using Gaussian mixture model to fit the risks within a given threshold, while fitting the extreme risks exceeding the threshold with a marked self-exciting point process. In the simulation study, we establish the consistencies of estimators and evaluate the performances of our proposed models by the accuracy of predicted VaR. Finally we apply our proposed models to analyze the behaviors of four real data sets. In order to illustrate our proposed approach can obtain an improved estimate for the VaR, CAViaR and the GARCH-EVT models are chosen for comparative analysis. The analysis shows that our proposed model have better performances than its competitors. [ABSTRACT FROM AUTHOR]

A generalized multinomial logit (G-MNL) model is proposed to alleviate the four challenges inherent to the conditional logit model, including (1) simultaneous unidentifiability, (2) the immediacy of decision-making, (3) the homogeneity of preferences in unobservable variables, and (4) the independence of irrelevant alternatives. However, the G-MNL model has some restrictions that are caused by the assumed logit scale of the lognormal distribution used in the G-MNL model. We propose a mixed logit with integrated Pareto-distributed scale (MIXL-iPS) model to address the restriction of the G-MNL model by introducing a logit scale in accordance with the Pareto distribution type I with an expected value of 1. We have clarified the mathematical properties and examined the distributional properties of the novel MIXL-iPS model. The results suggest that the MIXL-iPS model is a model in which the instability in the estimation of the G-MNL model is modified. Moreover, the apparent preference parameter was confirmed to have a skewed distribution in general in the MIXL-iPS model. In addition, we confirm that in the MIXL-iPS model, bounded rationality is reasonably well represented, as many individuals have below-average choice consistency. [ABSTRACT FROM AUTHOR]

This paper studies the ruin probabilities in a homogeneous continuous compound Poisson risk model which is adapted for the perturbed insurance risk model with standard Brownian motion. In such a model, we construct a martingale in terms of a differentiable exponential function based on the discounted and perturbed surplus process. We obtain the exponential upper bounds for the ruin probabilities using Martingale approach and provide a sharper exponential upper bound for the infinite time ruin probability. Moreover, we derive two asymptotic approximation formulas for the finite time ruin probability when claim size distribution belongs to some heavy-tailed families. Finally, several numerical examples are presented to show the effect of constant force of interest on the ruin probabilities and that our results are excellent and reliable. [ABSTRACT FROM AUTHOR]

Determining the extreme wind speed and basic wind speed in mountain areas is the fundamental topic in wind-resistant design for engineering structures. The traditional epochal approach commingles all types of wind's maximum speeds in a hybrid set regardless of their respective distributions. While the mountain wind climate is a typical mixed system that consists of local and synoptic wind events, differences in meteorological mechanisms lead to deviation in their wind speed distribution. Therefore, it is necessary to distinguish the mixed wind speed distribution and calculate the combined extreme wind speed. This study extends the extreme wind speed theory in mixed wind climates to the mountain wind field. The measured mountain wind data are classified into periodic thermally-driven winds caused by local thermal gradient, cooling windstorms driven by cold high pressure, and sudden intense winds caused by severe convection. Their respective distribution parameters are determined through the peaks-over-threshold approach with generalized Pareto distribution, and the combined extreme wind speed concluding all types of wind is obtained. The combined extreme wind speeds considering wind direction and attack angle are subsequently obtained. Results show that the combined value is a conservative estimation in mountain mixed wind climates. [ABSTRACT FROM AUTHOR]

The classical Pareto distribution is a positively skewed and right heavy-tailed lifetime distribution having many applications in various fields of science and social science. In this work, via the logarithmic transformed method, a new three-parameter lifetime distribution, an extension of classical Pareto distribution is generated. The different structural properties of the new distribution are studied. The model parameters are estimated by the method of maximum likelihood and Bayesian procedure. When all the three parameters of the distribution are unknown, the Bayes estimators cannot be obtained in a closed form, and hence, the Lindley's approximation under squared error loss function is used to compute the Bayes estimators. A Monte Carlo simulation study is also conducted to compare the performance of these estimators using mean square error. The application of the new distribution for modeling earthquake insurance and reliability data are illustrated using two real data sets. [ABSTRACT FROM AUTHOR]

The rich class of multivariate Pareto distributions forms the basis of recently introduced extremal graphical models. However, most existing literature on the topic is focused on the popular parametric family of Hüsler–Reiss distributions. It is shown that the Hüsler–Reiss family is in fact the only continuous multivariate Pareto model that exhibits the structure of a pairwise interaction model, justifying its use in many high‐dimensional problems. Along the way, useful insight is obtained concerning a certain class of distributions that generalize the Hüsler–Reiss family, a result of independent interest. [ABSTRACT FROM AUTHOR]

We propose new classes of tests for the Pareto type I distribution using the empirical characteristic function. These tests are U$$ U $$ and V$$ V $$ statistics based on a characterization of the Pareto distribution involving the distribution of the sample minimum. In addition to deriving simple computational forms for the proposed test statistics, we prove consistency against a wide range of fixed alternatives. A Monte Carlo study is included in which the newly proposed tests are shown to produce high powers. These powers include results relating to fixed alternatives as well as local powers against mixture distributions. The use of the proposed tests is illustrated using an observed data set. [ABSTRACT FROM AUTHOR]

In this paper we introduce the Exponential-Pareto mixture distribution. This distribution is associated as mixture of light and heavy-tailed data which arise in a wide class applications including risk analysis. Characteristic function, failure rate function, mean excess, conditional excess distribution are derived. It is proved that the limiting distribution of maxima among n values of rv’s with Exponential-Pareto distribution has Frechet-type form. The maximal likelihood estimation of parameters is discussed. The upper bound of uniform distance between Exponential-Pareto mixture and Pareto distributions is derived. [ABSTRACT FROM AUTHOR]

Probabilistic models for long-term estimations and deep learning models for short-term predictions have been evaluated and analyzed for ocean wave parameters. Estimation of design and operational wave parameters for long-term return periods is essential for various coastal and ocean engineering applications. Three probability distributions, namely generalized extreme value distribution (EV), generalized Pareto distribution (PD), and Weibull distribution (WD), have been considered in this work. The design wave parameter considered is the maximal wave height for a specified return period, and the operational wave parameters are the mean maximal wave height and the highest occurring maximal wave height. For precise location-based estimation, wave heights are considered from a nested wave model, which has been configured to have a 10 km spatial resolution. As per availability, buoy-observed data are utilized for validation purposes at the Agatti, Digha, Gopalpur, and Ratnagiri stations along the Indian coasts. At the stations mentioned above, the long short-term memory (LSTM)-based deep learning model is applied to provide short-term predictions with higher accuracy. The probabilistic approach for long-term estimation and the deep learning model for short-term prediction can be used in combination to forecast wave statistics along the coasts, reducing hazards. [ABSTRACT FROM AUTHOR]

The stress-strength reliability (SSR) model ϕ = P(Y < X) is used in numerous disciplines like reliability engineering, quality control, medical studies, and many more to assess the strength and stresses of the systems. Here, we assume X and Y both are independent random variables of progressively first failure censored (PFFC) data following inverse Pareto distribution (IPD) as stress and strength, respectively. This article deals with the estimation of SSR from both classical and Bayesian paradigms. In the case of a classical point of view, the SSR is computed using two estimation methods: maximum product spacing (MPS) and maximum likelihood (ML) estimators. Also, derived interval estimates of SSR based on ML estimate. The Bayes estimate of SSR is computed using the Markov chain Monte Carlo (MCMC) approximation procedure with a squared error loss function (SELF) based on gamma informative priors for the Bayesian paradigm. To demonstrate the relevance of the different estimates and the censoring schemes, an extensive simulation study and two pairs of real-data applications are discussed. [ABSTRACT FROM AUTHOR]

This paper conducts a systematic statistical analysis of the characteristics of the geographical empirical distributions for the numbers of both cumulative and daily confirmed COVID-19 cases and deaths at county, city, and state levels over a time span from January 2020 to June 2022. The mathematical heavy-tailed distributions can be used for fitting the empirical distributions observed in different temporal stages and geographical scales. The estimations of the shape parameter of the tail distributions using the Generalized Pareto Distribution also support the observations of the heavy-tailed distributions. According to the characteristics of the heavy-tailed distributions, the evolution course of the geographical empirical distributions can be divided into three distinct phases, namely the power-law phase, the lognormal phase I, and the lognormal phase II. These three phases could serve as an indicator of the severity degree of the COVID-19 pandemic within an area. The empirical results suggest important intrinsic dynamics of a human infectious virus spread in the human interconnected physical complex network. The findings extend previous empirical studies and could provide more strict constraints for current mathematical and physical modeling studies, such as the SIR model and its variants based on the theory of complex networks. [ABSTRACT FROM AUTHOR]

The aim of this paper is to obtain a Bayesian estimator of stress-strength reliability based on generalized order statistics for Pareto distribution. The dependence of the Pareto distribution support on the parameter complicates the calculations. Hence, in literature, one of the parameters is assumed to be known. In this paper, for the first time, two parameters of Pareto distribution are considered unknown. In computing the Bayesian confidence interval for reliability based on generalized order statistics, the posterior distribution has a complex form that cannot be sampled by conventional methods. To solve this problem, we propose an acceptance-rejection algorithm to generate a sample of the posterior distribution. We also propose a particular case of this model and obtain the classical and Bayesian estimators for this particular case. In this case, to obtain the Bayesian estimator of stress-strength reliability, we propose a variable change method. Then, these confidence intervals are compared by simulation. Finally, a practical example of this study is provided. [ABSTRACT FROM AUTHOR]

The generalized Pareto distribution is one of the most important distributions in statistics of extremes as it has wide applications in fields such as finance, insurance, and hydrology. This study proposes two new methods for estimating the shape parameter of the generalized Pareto distribution (GPD). The proposed methods use the shrinkage principle to adapt the existing empirical Bayesian with data-based prior and the likelihood moment method to obtain two estimators. The performance of the proposed estimators is compared with the existing estimators (i.e., maximum likelihood, likelihood moment estimators, etc.) for the shape parameter of the generalized Pareto distribution in a simulation study. The results show that the proposed estimators perform better for small to moderate number of exceedances in estimating shape parameter of the light-tailed distributions and competitive when estimating heavy-tailed distributions. The proposed estimators are illustrated with practical datasets from climate and insurance studies. [ABSTRACT FROM AUTHOR]

In order to guarantee the efficiency of life and reliability test in the case of censored data, and to control the total test time, an adaptive type-II progressive censored scheme is discussed. In this article, the classical estimation methods and Bayesian estimation methods are used to estimate the two unknown parameters, reliability function and hazard function of the Exponentiated Pareto distribution. In addition to the maximum likelihood estimation, the stochastic expectation-maximization (SEM) algorithm is also applied. Under two different loss functions, Lindley's approximation and importance sampling method are used to obtain Bayesian estimates. The Bayesian credible interval is constructed while the Bayesian estimate is evaluated by the Metropolis-Hastings method. The Monte Carlo method is applied to compare the performance of the estimation methods. Then a real life data set is analyzed. Finally, the selection criteria of various estimation methods are proposed. [ABSTRACT FROM AUTHOR]

The early health warning of a cable-stayed bridge is of great significance for discovering the abnormal condition of the structure, eliminating the risk factors, and ensuring the normal operation of the bridge in order to set a reasonable safety monitoring threshold to ensure the safety warning and condition assessment of the bridge structure. A method of dynamic early warning by considering the temperature effect is adopted in this paper on the basis of the benchmark threshold. Based on the long-term deflection monitoring data of a bridge in Wuhan, the generalized Pareto distribution (GPD) extreme value analysis theory is used to set the benchmark threshold. Then, by constructing the seasonal autoregressive integrated moving average (SARIMA) long-span bridge temperature effect prediction model, the reference threshold is dynamically adjusted. Finally, it is compared with the traditional fixed threshold monitoring system. The results show that the dynamic threshold has stronger adaptability to the monitoring of cable-stayed bridges and can also achieve effective monitoring of local mutations in other periods. Dynamic threshold early warning can reduce the shortcomings of traditional early warning methods such as underreporting and misreporting. At the same time, the GPD extreme value analysis theory overcomes the disadvantage that the extreme value information is not fully utilized. It has an important application value for bridge health monitoring. [ABSTRACT FROM AUTHOR]

Exponentiated models have been widely used in modeling various types of data such as survival data and insurance claims data. However, the exponentiated composite distribution models have not been explored yet. In this paper, we introduce an improvement of the one-parameter Inverse Gamma-Pareto composite model by exponentiating the random variable associated with the one-parameter Inverse Gamma-Pareto composite distribution function. The goodness-of-fit of the exponentiated Inverse Gamma-Pareto was assessed using three different insurance data sets. The two-parameter exponentiated Inverse Gamma-Pareto model outperforms the one-parameter Inverse Gamma-Pareto model in terms of goodness-of-fit measures for all datasets. In addition, the proposed exponentiated composite Inverse Gamma-Pareto model provides a very good fit with some well-known insurance datasets. [ABSTRACT FROM AUTHOR]

This paper considers the maximum number of weekly cases and deaths caused by the COVID-19 pandemic in Iraq from its outbreak in February 2020 until the first of July 2022. Some probability distributions were fitted to the data. Maximum likelihood estimates were obtained and the goodness of fit tests were performed. Results revealed that the maximum weekly cases were best fitted by the Dagum distribution, which was accepted by three goodness of fit tests. The generalized Pareto distribution best fitted the maximum weekly deaths, which was also accepted by the goodness of fit tests. The statistical analysis was carried out using the Easy-Fit software and Microsoft Excel 2019. [ABSTRACT FROM AUTHOR]

In this paper, a modified Pascoletti–Serafini scalarization approach, called MOP_MPS, is proposed to generate approximations of a Pareto front of bounded multi-objective optimization problems (MOPs). The objective is obtaining some points with an almost even distribution overall Pareto front. This algorithm is applied to six test problems with convex, non-convex, connected, and dis-connected Pareto fronts, and its results are compared with results of some famous algorithms. The results emphasize that MOP_MPS is effective and competitive in comparing with the other considered algorithms. In addition, it is shown that an optimal solution of a multiplicative programming problem is a properly Pareto optimal solution of an MOP. By considering this relation between MOPs and multiplicative programming problems (MPPs), another algorithm based on MOP_MPS, called MPP_MPS, is suggested for approximately solving non-linear MPPs in which functions multiplied are continuous and bounded from below. The computational results on seven problems of convex MPPs demonstrate that the algorithm is much better than a cut and bound algorithm presented by Shao and Ehrgott in terms of CPU time. [ABSTRACT FROM AUTHOR]

The accurate estimation of extreme precipitation frequency relies heavily on the quality of precipitation data. Conventional rain gauges provide in-situ observations, but they are susceptible to errors and are sparse or even absent in many parts of the world. Satellite-based precipitation products developed in recent years provide high-quality precipitation estimates on a regional and global scale. Before being used in such applications, it is vital to reduce errors by investigating their accuracy. In this study, we aimed to evaluate the application of the Integrated Multi-satellitE Retrievals for GPM (IMERG) product in the frequency analysis of extreme precipitation over Turkey. Initially, we evaluated the performance of the GPM IMERG over nine selected stations and deployed a bias correction procedure. Then, using the Generalized Pareto Distribution (GPD), we estimated 2-, 5-, 10-, 20-, 50-, and 100-year return levels. Implementation of the bias correction method yielded significant improvements in the results. The agreement of the GPM IMERG product with in-situ observations was between 0.24 and 0.65 on the Kling-Gupta Efficiency (KGE) metric and increased to the range of 0.54 to 0.75 after bias correction. Moreover, in the Mean Absolute Error (MAE) metric, the range of values changed from 5.30 to 1.39 mm/day and 5.80 to 1.10 mm/day. Furthermore, it noticeably reduced the error for most of the return periods. The error percentages between in-situ observations and bias-corrected IMERG products decreased below 25% at all stations for short return periods. Notably, at Ilgaz station, bias correction indicated an improvement of over 50% in error percentages for all return periods. The results demonstrated that GPD is a good solution, particularly for dealing with short time series, and suggest that IMERG can be a valuable alternative source for analyzing precipitation frequency over Turkey. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Marshall–Olkin Pareto type-I (MOPTI) distribution. Statistical attributes of the MOPTI distribution including the quantile function, mean residual life, and a new theorem for strength-stress measure are introduced. Five methods of estimation for the MOPTI parameters based on complete samples are presented. Furthermore, we explore the estimation of the MOPTI parameters under type-I and type-II censoring. Two Monte Carlo simulation studies are conducted to evaluate the performance of the estimation methods under complete and censored samples. A real-life data set is used to validate the proposed methods. [ABSTRACT FROM AUTHOR]

Dynamic economic emission dispatch（DEED） problem in power system is a kind of high-dimensional multiobjective optimization problem with large-scale constraints. The traditional evolutionary algorithm is easy to fall into local optimization, and the distribution and convergence of the obtained Pareto frontier are poor. In this paper, it fully explore the clonal selection principle of immune system, and propose a hybrid immune multi-objective optimization algorithm（HIMOA）. The proposed algorithm takes the traditional evolutionary algorithm as the basic framework.Since the deficiency of falling local optimization for the high-dimensional decision variables optimization, the external archive update mechanism is improved to preserve the excellent individuals from previous generations, and the cloning and Gaussian mutation strategy is adopted to strengthen the local exploitation ability, forcing effectively the HIMOA to jump out of the stagnant search state. In order to cope with the large-scale constraints, designing the fine-turning output power step by step to improve the feasibility of the evolutionary population. In the numerical simulation experiment, taking a 10-unit system as a test example, and compares HIMOA with the famous algorithms MODE,NSGAII, IMOEA/D-CH, ADEA, MOHDE＿SAT, MONNDE. The results show that HIMOA can provide a better Pareto solution to the 10-unit system of the DEED problem, and the convergence and distribution of the Pareto frontier obtained are better than other algorithms. The box diagram of each evaluation metric shows that HIMOA has better statistical characteristics than other algorithms. [ABSTRACT FROM AUTHOR]