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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]

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]

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 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]

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]

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]

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]

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]

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]

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]

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 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]

Climate change poses higher requirements on ocean engineering design, and reasonable estimation of design wave heights plays a crucial role in coastal protection and offshore engineering. Extreme value analysis is widely used in frequency calculations of wave parameters, among which the peak over threshold method based on the generalized Pareto distribution is proven to be an effective method, and the different selection of extreme wave samples in this method has a great influence on the calculation results. In this study, long-term significant wave height series were utilized to investigate the long-range correlation of significant wave heights, and thresholds were determined based on the changes of long-range correlations. This approach assumes that extreme events and non-extreme events are generally caused by different physical processes, where extreme events result from massive disturbances leading to abnormal states, and long-range correlations are not affected or minimally affected by extreme events. Thus, thresholds can be determined based on changes of long-range correlations by removing extreme events. Comparing this method to graphical diagnostic techniques, we demonstrated its rationality in determining extreme wave height thresholds. Moreover, the automatic threshold selection offered by this method helps to mitigate errors associated with subjective judgments in traditional approaches. [ABSTRACT FROM AUTHOR]

Precipitation modeling holds significant importance in various fields such as agriculture, animal husbandry, weather derivatives, hydrology, and risk and disaster preparedness. Stochastic precipitation generators (SPGs) represent a class of statistical models designed to generate synthetic data capable of simulating dry and wet precipitation stretches for a long duration. The construction of Hidden Markov Models (HMMs), which treat latent meteorological circumstances as hidden states, is an efficient technique for simulating precipitation. Considering that there are many choices of emission distributions used to generate positive precipitation, the characteristics of different distributions for simulating positive precipitation have not been fully explored. The paper includes a simulation study that demonstrates how the Pareto distribution, when used as the distribution for generating positive precipitation, addresses the limitations of the exponential and gamma distributions in predicting heavy precipitation events. Additionally, the Pareto distribution offers flexibility through adjustable parameters, making it a promising option for precipitation modeling. We can estimate parameters in HMMs using forward–backward algorithms, Variational Bayes Expectation-Maximization (VBEM), and Stochastic Variational Bayes (SVB). In the Xilingol League, located in the central part of the Inner Mongolia Autonomous Region, China, our study involved data analysis to identify crucial locations demonstrating a robust correlation and notable partial correlation between the Normalized Difference Vegetation Index (NDVI) and annual precipitation. We performed fitting of monthly dry days ratios and monthly precipitation using seasonal precipitation and year-round precipitation data at these crucial locations. Subsequently, we conducted precipitation predictions for the daily, monthly, and annual time frames using the new test dataset observations. The study concludes that the SPG fits the monthly dry-day ratio better for annual daily precipitation data than for seasonal daily precipitation data. The fitting error for the monthly dry day ratio corresponding to annual daily precipitation data is 0.053 (exponential distribution) and 0.066 (Pareto distribution), while for seasonal daily precipitation data, the fitting error is 0.14 (exponential distribution) and 0.15 (Pareto distribution). The exponential distribution exhibits the poorest performance as a model for predicting future precipitation, with average errors of 2.49 (daily precipitation), 40.62 (monthly precipitation), and 130.40 (annual precipitation). On the other hand, the Pareto distribution demonstrates the best overall predictive performance, with average errors of 0.69 (daily precipitation), 34.69 (monthly precipitation), and 66.42 (annual precipitation). The results of this paper can provide decision support for future grazing strategies in the Xilingol League. [ABSTRACT FROM AUTHOR]

Minimizing a company's operational risk by optimizing the performance of the manufacturing and distribution supply chain is a complex task that involves multiple elements, each with their own supply line constraints. Traditional approaches to optimization often assume determinism as the underlying principle. However, this paper, adopting an entropy approach, emphasizes the significance of subjective and objective uncertainty in achieving optimized decisions by incorporating stochastic fluctuations into the supply chain structure. Stochasticity, representing randomness, quantifies the level of uncertainty or risk involved. In this study, we focus on a processing production plant as a model for a chain of operations and supply chain actions. We consider the stochastically varying production and transportation costs from the site to the plant, as well as from the plant to the customer base. Through stochastic optimization, we demonstrate that the plant producer can benefit from improved financial outcomes by setting higher sale prices while simultaneously lowering optimized production costs. This can be accomplished by selectively choosing producers whose production cost probability density function follows a Pareto distribution. Notably, a lower Pareto exponent yields better supply chain cost optimization predictions. Alternatively, a Gaussian stochastic fluctuation may be proposed as a more suitable choice when trading off optimization and simplicity. Although this may result in slightly less optimal performance, it offers advantages in terms of ease of implementation and computational efficiency. [ABSTRACT FROM AUTHOR]

The reliability of extreme wind speed predictions at large mean recurrence intervals (MRI) is assessed by bootstrapping samples from representative known distributions. The classical asymptotic generalized extreme value distribution (GEV) and the generalized Pareto (GPD) distribution are compared with a contemporary sub-asymptotic Gumbel distribution that accounts for incomplete convergence to the correct asymptote. The sub-asymptotic model is implemented through a modified Gringorten method for epoch maxima and through the XIMIS method for peak-over-threshold values. The mean bias error is shown to be minimal in all cases, so that the variability expressed by the standard error becomes the principal reliability metric. Peak-over-threshold (POT) methods are shown to always be more reliable than epoch methods due to the additional sub-epoch data. The generalized asymptotic methods are shown to always be less reliable than the sub-asymptotic methods by a factor that increases with MRI. This study reinforces the previously published theory-based arguments that GEV and GPD are unsuitable models for extreme wind speeds by showing that they also provide the least reliable predictions in practice. A new two-step Weibull-XIMIS hybrid method is shown to have superior reliability. [ABSTRACT FROM AUTHOR]

The digitalization of bank data and financial operations creates a large risk of loss. Losses due to the risk of errors in the bank's digital system need to be mitigated through the readiness of reserve funds. The determination of reserve funds needs to be optimized so that there is no large excess of reserve funds. Then the rest of the reserve fund allocation can be used as an investment fund by the bank to obtain additional returns or profits. This study aims to optimize the reserve fund allocation for digital banking transactions. In this case, the decision variable is value reserved based on potential loss of each digital banking, and the objective function is defined as minimizing reserve fund allocation. Furthermore, some conditions that become limitation are rules of Basel II, Basel III, and Article 71 paragraph 1 of the Limited Liability Company Law. Since the objective function can be expressed as a linear function, in this paper, linear programming optimization approach is thus employed considering Extreme Value-at-Risk (EVaR) constraints. In the use of EVaR approach in the digital banking problem, it is found that the loss meets the criteria of extreme data based on the Generalized Pareto Distribution (GPD). The strength of reserve funds using linear programming optimization with EVaR constraints is the consideration of potential losses from digital banking risks that are minimized so that the allocation of company funds becomes optimum. While the determination of reserve funds with a standard approach only considers historical profit data, this can result in excessive reserve funds because they are not considered potential risks in the future period. For the numerical experiment, the following risk data are used in the modeling, i.e., the result of a sample simulation of digital banking losses due to the risk of system downtime, system timeout, external failure, and operational user failure. Therefore, the optimization model with EVaR constraints produces an optimal reserve fund value, so that the allocation of bank reserve funds becomes efficient. This provides a view for banking companies to avoid the worst risk, namely collapse due to unbalanced mandatory reserve funds. [ABSTRACT FROM AUTHOR]

Accurate parameter estimation is essential for modeling the statistical characteristics of ocean clutter. Common parameter estimation methods in generalized Pareto distribution models have limitations, such as restricted parameter ranges, lack of closed-form expressions, and low estimation accuracy. In this study, the particle swarm optimization (PSO) algorithm is used to solve the non-closed-form parameter estimation equations of the generalized Pareto distribution. The goodness-of-fit experiments show that the PSO algorithm effectively solves the non-closed parameter estimation problem and enhances the robustness of fitting the generalized Pareto distribution to heavy-tailed oceanic clutter data. In addition, a new parameter estimation method for the generalized Pareto distribution is proposed in this study. By using the difference between the statistical histogram of the data and the probability density function/cumulative distribution function of the generalized Pareto distribution as the target, an adaptive function with weighted coefficients is constructed to estimate the distribution parameters. A hybrid PSO (HPSO) algorithm is used to search for the best position of the fitness function to achieve the best parameter estimation of the generalized Pareto distribution. Simulation analysis shows that the HPSO algorithm outperforms the PSO algorithm in solving the parameter optimization task of the generalized Pareto distribution. A comparison with other traditional parameter estimation methods for generalized Pareto distribution shows that the HPSOHPSO algorithm exhibits strong parameter estimation performance, is efficient and stable, and is not limited by the parameter range. [ABSTRACT FROM AUTHOR]

A critical stage in drought risk assessment is the measurement of drought hazard, the probability of occurrence of a potentially damaging event. The standard approach to assess drought hazard is based on the standardized precipitation index (SPI) and a drought intensity classification established according to a fixed set of SPI values. We show that this method does not allow for the assessment of region-specific hazards, and we propose an alternative method based on the extreme value theory. We model precipitation using an extreme value mixture model, with a normal distribution for the bulk, and a generalized Pareto distribution for the upper and lower tails. The model estimation allows us to identify the threshold value below which precipitation can be qualified as extreme. The quantile function is used to measure the intensity of each category of droughts and calculate the drought hazard index (DHI). By construction, the DHI value varies according to the specific characteristics of the left tail of the precipitation distribution. To test the relevance of our approach, we estimate the DHI over a gridded set of rainfall data covering West Africa, a large and climatically heterogeneous region. The results show that our mixture model fits the data better than the model used for SPI calculation. In particular, our model performs better to identify extreme precipitation in the left tail of the distribution. The DHI map highlights clusters of high drought hazard located in the central part of the region under study. [ABSTRACT FROM AUTHOR]

Nickel superalloys occupy a reasonably broad niche in the industry. One of this group's most common and well-known alloys is Inconel 718. Parts from Inconel 718 are used in aerospace, energy, automotive, and some other vital industries, which creates a demand for research and improvement of the machining conditions of this alloy. This article is devoted to the systematization and generalization of the accumulated experience of machining of Inconel 718 at turning operation. The research methodology is based on the Pareto distribution. In the study, more than 50 articles devoted to turning Inconel 718 were analyzed. The tool materials, methods, and types of coating used in turning Inconel 718 were analyzed. Finite element method modeling of processing processes has been considered. The trends in the selection of cutting parameters and the geometry of the cutting tool and finite element method modeling of processing processes have been considered. Lacunae for promising future research were formulated. [ABSTRACT FROM AUTHOR]

The expansion of urban areas and the increasing frequency and magnitude of intense rainfall events are anticipated to contribute to the widespread escalation of urban flood risk across the globe. To effectively mitigate future flood risks, it is crucial to combine a comprehensive examination of intense rainfall events in urban areas with the utilization of detailed hydrodynamic models. This study combines extreme value analysis techniques applied to rainfall data ranging from sub-hourly to daily durations with a high-resolution flood modelling analysis at the building level in the centre of Thessaloniki, Greece. A scaling procedure is employed to rainfall return levels assessed by applying the generalised extreme value (GEV) distribution to annual maximum fine-temporal-scale data, and these scaling laws are then applied to more reliable daily rainfall return levels estimated by means of the generalised Pareto distribution (GPD), in order to develop storm profiles with durations of 1 h and 2 h. The advanced flood model, CityCAT, is then used for the simulation of pluvial flooding, providing reliable assessments of building-level exposure to flooding hazards. The results of the analysis conducted provide insights into flood depths and water flowpaths in the city centre of Thessaloniki, identifying major flowpaths along certain main streets resulting in localised flooding, and identifying around 165 and 186 buildings highly exposed to inundation risk in the study area for 50-year storm events with durations of 1 h and 2 h, respectively. For the first time in this study area, a detailed analysis of extreme rainfall events is combined with a high-resolution Digital Terrain Model (DTM), used as an input into the advanced and fully featured CityCAT hydrodynamic model, to assess critical flowpaths and buildings at high flood risk. The results of this study can aid in the planning and design of resilient solutions to combat urban flash floods, as well as contribute to targeted flood damage mitigation and flood risk reduction. [ABSTRACT FROM AUTHOR]

Skewed probability distributions are important when modeling skewed data sets because they provide a way to describe the shape of the distribution and estimate the likelihood of extreme events. Asymmetric probability distributions have the potential to handle and assess problems in actuarial risk assessment and analysis. To that end, we present a new right-skewed one-parameter distribution. In this work and for this purpose, a right-skewed probability distribution was derived and analyzed. The new distribution outperformed the exponential distribution, the Pareto distribution, the Chen distribution, and others in the field of actuarial risk analysis. Some useful key risk indicators are considered and analyzed to analyze the risks and for comparison with the competitive model. Several actuarial risk functions and indicators are evaluated and analyzed using the U.K. insurance claims data set. The process of risk assessment and analysis was carried out using a comprehensive simulation. For the purposes of distributional validity, a modified chi-squared type test is presented and employed in the testing process. The new, modified chi-squared type test that is used is simply an extension of the Rao–Robson–Nikulin test. In this work, the distributional validity is presented and analyzed under right-skewed censored and uncensored data sets. [ABSTRACT FROM AUTHOR]

Income distribution models can be useful for describing the economic properties of a population. In this study, three-part composite Pareto models are fitted to the income distribution in Malaysia for the years 2007, 2009, 2012, 2014, and 2016. The three-part composite Pareto models divide the population into three parts, each following a different distribution model. The lower part follows the inverse Pareto distribution, the upper part follows the Pareto distribution, and the middle part follows another unspecified distribution model. For application in income data, the use of Gaussian mixture distribution is proposed for the middle part, making the inverse Pareto–Gaussian mixture-Pareto distribution model semi-parametric. From the model, it is found that the levels of income inequality in the lower and upper income groups decrease over the period of study. Additionally, the proportion of data following the inverse Pareto distribution in the model is highly correlated with the official absolute poverty incidence. [ABSTRACT FROM AUTHOR]

A memristor is a kind of nonlinear electronic component. Parameter identification for memristive chaotic systems is a multi-dimensional variable optimization problem. It is one of the key issues in chaotic control and synchronization. To identify the unknown parameters accurately and quickly, we introduce, in this paper, a modified Pelican Optimization Algorithm (POA) called the fractional-order chaotic Pareto Pelican Optimization Algorithm (FPPOA). First, the pelican population's diversity is augmented with the integration of a fractional chaotic sequence. Next, the utilization of the Pareto distribution is incorporated to alter the hunting strategy of pelicans in the POA. These measures are effective in hastening the speed of finding an optimal solution and circumventing local optimization issues. Thirdly, the FPPOA is used to determine the values of the parameters of the simplest memristive chaotic system, which has a property of conditional symmetry. The proposed algorithm was evaluated during simulations, where it was utilized to solve six objective functions of varying unimodal and multimodal types. The performance of the FPPOA exceeds three traditional swarm intelligence optimization algorithms. In the parameter identification experiment, the results for the parameters with the FPPOA had error rates all within a 1% range. Extensive testing shows that our new strategy has a faster rate of convergence and better optimization performance than some other traditional swarm algorithms. [ABSTRACT FROM AUTHOR]

To obtain the load spectrum of the traction resistance of the three-point suspension device under tractor-plowing conditions, a load spectrum extrapolation method based on a genetic algorithm optimal threshold selection is proposed. This article first uses a pin force sensor to measure the plowing resistance of the tractor's three-point suspension device under plowing conditions and preprocesses the collected load signal. Next, a genetic algorithm is introduced to select the threshold based on the Peak Over Threshold (POT) extremum extrapolation model. The Generalized Pareto Distribution (GPD) fits the extreme load distribution that exceeds the threshold range, generating new extreme points that follow the GPD distribution to replace the extreme points in the original data, achieving the extrapolation of the load spectrum. Finally, the loading spectrum that can be achieved on the test bench is obtained based on the miner fatigue theory and accelerated life theory. The results show that the upper threshold of the time-domain load data obtained by the genetic algorithm is 10.975 kN, and the grey correlation degree is 0.7249. The optimal lower threshold is 8.5455 kN, the grey correlation degree is 0.7722, and the fitting effect of the GPD distribution is good. The plowing operation was divided into five stages: plowing tool insertion, acceleration operation, constant speed operation, deceleration operation, and plowing tool extraction. A traction resistance loading spectrum that can be achieved on the test bench was developed. The load spectrum extrapolation method based on the genetic algorithm optimal threshold selection can improve the accuracy of threshold selection and achieve the extrapolation and reconstruction of the load spectrum. After processing the extrapolated load spectrum, it can be transformed into a load spectrum that can be recognized by the test bench. [ABSTRACT FROM AUTHOR]

Cryptocurrencies are said to be very risky, and so are the currencies of emerging economies, including the South African rand. The steady rise in the movement of South Africans' investments between the rand and BitCoin warrants an investigation as to which of the two currencies is riskier. In this paper, the Generalised Pareto Distribution (GPD) model is employed to estimate the Value at Risk (VaR) and the Expected Shortfall (ES) for the two exchange rates, BitCoin/US dollar (BitCoin) and the South African rand/US dollar (ZAR/USD). The estimated risk measures are used to compare the riskiness of the two exchange rates. The Maximum Likelihood Estimation (MLE) method is used to find the optimal parameters of the GPD model. The higher extreme value index estimate associated with the BTC/USD when compared with the ZAR/USD estimate, suggests that the BTC/USD is riskier than the ZAR/USD. The computed VaR estimates for losses of $0.07, $0.09, and $0.16 per dollar invested in the BTC/USD at 90%, 95%, and 99% compared to the ZAR/USD's $0.02, $0.02, and $0.03 at the respective levels of significance, confirm that BitCoin is riskier than the rand. The ES (average losses) of $0.11, $0.13, and $0.21 per dollar invested in the BTC/USD at 90%, 95%, and 99% compared to the ZAR/USD's $0.02, $0.02, and $0.03 at the respective levels of significance further confirm the higher risk associated with BitCoin. Model adequacy is confirmed using the Kupiec test procedure. These findings are helpful to risk managers when making adequate risk-based capital requirements more rational between the two currencies. The argument is for more capital requirements for BitCoin than for the South African rand. [ABSTRACT FROM AUTHOR]

In this paper, we emphasize a new one-parameter distribution with support as [ 1 , + ∞) . It is constructed from the inverse method applied to an understudied one-parameter unit distribution, the unit Teissier distribution. Some properties are investigated, such as the mode, quantiles, stochastic dominance, heavy-tailed nature, moments, etc. Among the strengths of the distribution are the following: (i) the closed-form expressions and flexibility of the main functions, and in particular, the probability density function is unimodal and the hazard rate function is increasing or unimodal; (ii) the manageability of the moments; and, more importantly, (iii) it provides a real alternative to the famous Pareto distribution, also with support as [ 1 , + ∞) . Indeed, the proposed distribution has different functionalities but also benefits from the heavy-right-tailed nature, which is demanded in many applied fields (finance, the actuarial field, quality control, medicine, etc.). Furthermore, it can be used quite efficiently in a statistical setting. To support this claim, the maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, Cramér–Von Mises, least squares, weighted least-squares, maximum product of spacing, minimum spacing absolute distance, and minimum spacing absolute-log distance estimation methods are examined to estimate the unknown unique parameter. A Monte Carlo simulation is used to compare the performance of the obtained estimates. Additionally, the Bayesian estimation method using an informative gamma prior distribution under the squared error loss function is discussed. Data on the COVID mortality rate and the timing of pain relief after receiving an analgesic are considered to illustrate the applicability of the proposed distribution. Favorable results are highlighted, supporting the importance of the findings. [ABSTRACT FROM AUTHOR]

This article analyzes six probability distributions from the Generalized Pareto family, with three, four and five parameters, with the main purpose of identifying other distributions from this family with applicability in flood frequency analysis compared to the distribution already used in the literature from this family such as Generalized Pareto Type II and Wakeby. This analysis is part of a larger and more complex research carried out in the Faculty of Hydrotechnics regarding the elaboration of a norm for flood frequency analysis using the linear moments method. In Romania, the standard method of parameter estimation is the method of ordinary moments, thus the transition from this method to the method of linear moments is desired. All the necessary elements for the distribution use are presented, such as the probability density functions, the complementary cumulative distribution functions, the quantile functions, and the exact and approximate relations for estimating parameters, for both methods of parameter estimation. All these elements are necessary for a proper transition between the two methods, especially since the use of the method of ordinary moments is done by choosing the skewness of the observed data depending on the origin of the maximum flows. A flood frequency analysis case study, using annual maximum and annual exceedance series, was carried out for the Prigor River to numerically present the analyzed distributions. The performance of this distribution is evaluated using a linear moments diagram. [ABSTRACT FROM AUTHOR]

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

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

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

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

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

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

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

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

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

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

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

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

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

The convergence rate in the famous Rényi theorem is studied by means of the Stein method refinement. Namely, it is demonstrated that the new estimate of the convergence rate of the normalized geometric sums to exponential law involving the ideal probability metric of the second order is sharp. Some recent results concerning the convergence rates in Kolmogorov and Kantorovich metrics are extended as well. In contrast to many previous works, there are no assumptions that the summands of geometric sums are positive and have the same distribution. For the first time, an analogue of the Rényi theorem is established for the model of exchangeable random variables. Also within this model, a sharp estimate of convergence rate to a specified mixture of distributions is provided. The convergence rate of the appropriately normalized random sums of random summands to the generalized gamma distribution is estimated. Here, the number of summands follows the generalized negative binomial law. The sharp estimates of the proximity of random sums of random summands distributions to the limit law are established for independent summands and for the model of exchangeable ones. The inverse to the equilibrium transformation of the probability measures is introduced, and in this way a new approximation of the Pareto distributions by exponential laws is proposed. The integral probability metrics and the techniques of integration with respect to sign measures are essentially employed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a general class of bivariate proportional hazard distributions, which is based on the family of asymmetric proportional hazard distributions and the bivariate Pareto copula. Distributional properties of the bivariate proportional hazard distribution are derived. We specialize the bivariate proportional hazard family of distributions to the normal case, and so we introduce the bivariate proportional hazard normal distribution. Parameter estimation by the maximum likelihood method of the bivariate proportional hazard normal distribution is then discussed. Finally, an application of the new bivariate distribution to real data is considered for illustrative purposes. [ABSTRACT FROM AUTHOR]

The identification of the appropriate distribution of faults is important for ensuring the reliability of a software system and its maintenance. It has been observed that different distributions explain faults in different types of software. Faults in large and complex software systems are best represented by Pareto distribution, whereas Weibull distribution fits enterprise software well. An analysis of faults in open-source software endorses generalized Pareto distribution. This paper presents a model, called the Tsallis distribution, derived using the maximum-entropy principle, which explains faults in many diverse software systems. The effectiveness of Tsallis distribution is ascertained by carrying out experiments on many real data sets from enterprise and open-source software systems. It is found that Tsallis distribution describes software faults better and more precisely than Weibull and generalized Pareto distributions, in both cases. The applications of the Tsallis distribution in (i) software fault-prediction using the Bayesian inference method, and (ii) the Goal and Okumoto software-reliability model, are discussed. [ABSTRACT FROM AUTHOR]

In this study, inspection planning of deteriorating bridges is optimized to determine the inspection application times and methods based on various objectives. These objectives can be formulated by considering the probabilistic structural performance and service life after inspection and maintenance. Probabilistic structural performance and service life prediction are generally based on the probability of failure (or reliability). However, there are difficulties associated with optimizing inspection planning when a low probability of failure is estimated. In this study, we address inspection planning using extrapolation approaches to efficiently compute a low probability of failure. The inspection planning method proposed in this study determines the inspection application times for a given inspection method. We investigated the applicability of direct Monte Carlo simulation (MCS), subset simulation, and two extrapolation approaches (i.e., kernel density estimation (KDE) and KDE combined with generalized Pareto distribution (GPD)) for inspection planning. The probability of failure for optimum inspection planning was based on the damage detection-based state function and extended service life-based state function. These state functions were formulated by considering damage propagation, damage detection by inspections, and service life extensions by maintenance. Illustrative applications to general examples and an existing bridge are provided to investigate the effects of approaches for computing the failure probability on the accuracy and variation of the optimum inspection application times. Finally, the most appropriate approach for optimum inspection planning was determined considering the accuracy and reliability of the solution, computational efficiency, and the applicability of the probabilistic optimization process. The presented investigations revealed that KDE is more appropriate than MCS and the combination of KDE and GPD for optimum inspection planning. [ABSTRACT FROM AUTHOR]

During its 330 years of history, parametric distributions have been useful for survival and reliability analyses. In this paper, we comprehensively review the historical backgrounds and statistical properties of a number of parametric distributions used in survival and reliability analyses. We provide encyclopedic coverage of the important parametric distributions, which is more extensive than the existing textbooks on survival and reliability analyses. We also explain how these distributions have been adopted in survival and reliability analyses with original and state-of-the-art references. We cover the exponential, Weibull, Rayleigh, lognormal, log-logistic, gamma, generalized gamma, Pareto (types I, II, and IV), Hjorth, Burr (types III and XII), Dagum, exponential power, Gompertz, Birnbaum-Saunders, exponential-logarithmic, piecewise exponential, generalized exponential, exponentiated Weibull, generalized modified Weibull, and spline distributions. We analyze a real dataset for illustration. [ABSTRACT FROM AUTHOR]