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

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]

A jointly censored sample is a very useful sampling technique in conducting comparative life tests of the products, its efficiency appears in permitting the selection of two samples from two manufacturing lines at the same time and conducting a life-testing experiment. This article presents estimation information of the joint generalized Pareto distributions parameters using Type-II progressive censoring scheme, which is carried out with binomial removal. The generalized Pareto distribution has many applications in different fields. We outline the problem of parameter estimation using the frequentest maximum likelihood and the Bayesian estimation methods. Furthermore, different interval estimation methods for estimating the four parameters were used: the asymptotic property of the maximum likelihood estimator, the credible confidence intervals, and the Bootstrap confidence intervals. The detailed numerical simulations have been considered to compare the performance of the proposed estimates. In addition, the applicability of the joint generalized Pareto censored model has been performed by applying a real data example. [ABSTRACT FROM AUTHOR]

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

The problem of 3D coverage in a wireless sensor network (WSN) has always been an urgent problem to be solved. A novel compact particle swarm optimization algorithm (ncPSO) to solve this problem is proposed in this paper. This algorithm uses a Pareto distribution to describe the position of particle swarms. The ncPSO reduces memory usage compared to traditional heuristics. The ncPSO using the Pareto distribution is less likely to fall into local optima than other compact algorithms using the Gaussian distribution. We also add Gaussian perturbation strategy to the algorithm to better avoid the algorithm falling into local optimum. Among the test functions of CEC2013, the ncPSO achieves remarkable optimization ability on most test functions. Finally, we apply ncPSO to the 3D coverage problem of sensors. Compared with other algorithms, the ncPSO achieves satisfactory results. [ABSTRACT FROM AUTHOR]

The Pareto distribution is widely used to model industrial, biological, engineering, and other various types of data. A new generalized model, namely the neutrosophic Pareto distribution (NPD), is developed in this article. The proposed model is a neutrosophic variant of the classical Pareto distribution, potentially useful for analyzing vague, unclear, indeterminate, or imprecise data. The structure form of the proposed distribution is skewed to the right and determined to be unimodal. Several characteristics of the NPD are investigated under the neutrosophic framework. The expressions for basic properties such as mean, variance, raw moments, and shape coefficients are obtained. The maximum likelihood approach is presented for estimating the imprecise distributional parameters of the proposed model. The extended notions of the NPD are explained with various key functions in the domain of applied statistical methods. Finally, the practical benefits of NPD are proven by analyzing two real datasets. [ABSTRACT FROM AUTHOR]

In the lifetime and reliability experiments, the censored samples play a fundamental and important role in order to control time and cost. The researchers developed the censored sample schemes to solve the problems that arise by applying the previous methods. Recently, Górny and Cramer (2018) proposed a new general type of censored sample called Type-II unified progressive hybrid censored sample. In this paper, we present an overview of the Type-II unified progressive hybrid censored sample. We used this censored sample to compute the maximum likelihood estimates of unknown parameters from the Pareto distribution, as well as Bayesian estimates for unknown parameters under three different error loss functions. The point and interval Bayesian predictions one- and two-sample Bayesian predictions from the Pareto distribution are shown. Simulation studies are carried out to compare the efficacy of the various inference approaches. Finally, real data sets are examined to determine the applicability of the proposed model and various estimating approaches. [ABSTRACT FROM AUTHOR]

This paper uses extreme value theory and exponential generalised autoregressive score models to estimate the tail extremes of financial return series. The peak-over-threshold method based on the generalised pareto distribution is combined with the EGAS models and the nonparametric quantile method is used to determine the thresholds in the POT method, which is used to calculate the value-at-risk of financial markets and to perform backtesting. The empirical analysis was conducted on the soybean oil, rapeseed oil, and palm oil futures indices in the Chinese futures market. The study demonstrated that the EGAS-POT models based on nonparametric quantile thresholds can effectively characterise tail risk and provide a feasible measure of risk for investors. [ABSTRACT FROM AUTHOR]

With the development of wireless communication technology, video and multimedia have become an integral part of visual communication design. Designers want higher interactivity, diversity, humanization, and plurality of attributes in the process of visual communication. This makes the process of visual communication have high requirements for the quality and real-time data transmission. To address the problem of transmitting HD video in a heterogeneous wireless network with multiple concurrent streams to improve the transmission rate and thus enhance the user experience, with the optimization goal of minimizing the system transmission delay and the delay difference between paths, the video sender and receiver are jointly considered, and the video transmission rate and the cache size at the receiver are adaptively adjusted to improve the user experience, and a cooperative wireless communication video transmission based on the control model for video transmission based on cooperative wireless communication is established, and video streams with self-similarity and long correlation are studied based on Pareto distribution and P / P / l queuing theory, based on which an adaptive streaming decision method for video streams in heterogeneous wireless networks is proposed. Simulation results show that the proposed multistream concurrent adaptive transmission control method for heterogeneous networks is superior in terms of delay and packet loss rate compared with the general load balancing streaming decision method, in terms of transmission efficiency and accuracy. [ABSTRACT FROM AUTHOR]

In this paper, a new generalization of the Generalized Pareto distribution is proposed using the generator suggested in [1], named as Khalil Extended Generalized Pareto (KEGP) distribution. Various shapes of the suggested model and important mathematical properties are investigated that includes moments, quantile function, moment-generating function, measures of entropy, and order statistics. Parametric estimation of the model is discussed using the technique of maximum likelihood. A simulation study is performed for the assessment of the maximum likelihood estimates in terms of their bias and mean squared error using simulated sample estimates. The practical applications are illustrated via two real data sets from survival and reliability theory. The suggested model provided better fits than the other considered models. [ABSTRACT FROM AUTHOR]

In this article, we consider estimation of the parameters of a generalized Pareto distribution and some lifetime indices such as those relating to reliability and hazard rate functions when the failure data are progressive first-failure censored. Both classical and Bayesian techniques are obtained. In the Bayesian framework, the point estimations of unknown parameters under both symmetric and asymmetric loss functions are discussed, after having been estimated using the conjugate gamma and discrete priors for the shape and scale parameters, respectively. In addition, both exact and approximate confidence intervals as well as the exact confidence region for the estimators are constructed. A practical example using a simulated data set is analyzed. Finally, the performance of Bayes estimates is compared with that of maximum likelihood estimates through a Monte Carlo simulation study. [ABSTRACT FROM AUTHOR]

Recommender systems represent a critical field of AI technology applications. The core function of a recommender system is to recommend items of interest to users, but if it is only user history-based (purchasing or browsing data), it can only recommend similar products to a user, which makes the user feel fatigued (creating so-called "Information Cocoons"). Besides, transaction data (purchasing or browsing data) in various fields usually follow Pareto distributions. Accordingly, 20% of products are purchased or viewed a greater number of times (short-head items), while the remaining 80% of products are purchased or viewed less frequently (long-tail items). Using the traditional recommendation method, considering only the accuracy of recommendations, the coverage rate is relatively low, and most of the recommended items are short-head items. The long-tail item recommendation method not only considers the recommendation of short-head items but also considers recommending more long-tail items to users, thus improving the coverage and diversity of the recommendation results. Long-tail item recommendation research has become a frontier issue in recommendation systems in recent years. While the current research paper is still scarce, there have been related research achievements in top-level conferences in the field of computers, such as VLDB and IJCAI. Due to the fact that there is no review literature in this field, to allow readers to better understand the research status of the long-tail item recommendation method, this paper summarizes the progress of the research on long-tail item recommendation methods (from clustering-based, which began in 2008, to deep learning-based methods, which began in 2020) and the future directions associated with this research. [ABSTRACT FROM AUTHOR]

The extreme value theory (EVT) has been used to model and measure the distribution of extreme minima of Byco Petroleum in the Pakistan stock market over the period from 2005 to 2012. This paper covers the investigation of distributions that are mostly used in finance including the generalized extreme value (GEV), generalized logistics (GL), and generalized Pareto (GPA) distribution. L-moment ratio diagram is being used to find the appropriate distributions among the distributions. L-moment diagram depicts that GEV and GL distributions are suitable to represent the extremes of Byco Petroleum Pakistan Limited. Thereafter, the probability weighted moment (PWM) method has been used in order to estimate the parameters of probability distributions. Furthermore, Anderson–Darling (AD) goodness-of-fit test is employed to test the goodness of fit among GEV and GL distributions, and it is clear from the results that the GL distribution is more reliable and applicable for extreme minima of Byco Petroleum Company in the Pakistan stock exchange market. EVT and traditional methods are used for value-at-risk (VaR) analysis. The analysis indicates that EVT methods are more suitable for risk measurement in comparison with traditional methods. [ABSTRACT FROM AUTHOR]

This paper introduced a relatively new mixture distribution that results from a mixture of Fréchet–Weibull and Pareto distributions. Some properties of the new statistical model were derived, such as moments with their related measures, moment generating function, mean residual life function, and mean deviation. Furthermore , different estimation methods were introduced for determining the unknown parameters of the proposed model. Finally, we introduced three real data sets which were applied to our distribution and compared them with other well-known statistical competitive models to show the superiority of our model for fitting the three real data sets, and we can clearly see that our distribution outperforms its competitors. Also, to verify our results, we carried out the existence and uniqueness test to the log-likelihood to determine whether the roots are global maximum or not. [ABSTRACT FROM AUTHOR]

In this study, we model a heterogeneous population assuming the three-component mixture of the Pareto distributions assuming type I censored data. In particular, we study some statistical properties (such as various entropies, different inequality indices, and order statistics) of the three-component mixture distribution. The ML estimation and the Bayesian estimation of the mixture parameters have been performed in this study. For the ML estimation, we used the Newton Raphson method. To derive the posterior distributions, different noninformative priors are assumed to derive the Bayes estimators. Furthermore, we also discussed the Bayesian predictive intervals. We presented a detailed simulation study to compare the ML estimates and Bayes estimates. Moreover, we evaluated the performance of different estimates assuming various sample sizes, mixing weights and test termination times (a fixed point of time after which all other tests are dismissed). The real-life data application is also a part of this study. [ABSTRACT FROM AUTHOR]

The generalised Pareto distribution (GPD) offers a family of probability spaces which support threshold exceedances and is thus suitable for modelling high-end actuarial risks. Nonetheless, its distributional continuity presents a critical limitation in characterising data of discrete forms. Discretising the GPD, therefore, yields a derived distribution which accommodates the count data while maintaining the essential tail modelling properties of the GPD. In this paper, we model non-life insurance claims under the three-parameter discrete generalised Pareto (DGP) distribution. Data for the study on reported and settled claims, spanning the period 2012–2016, were obtained from the National Insurance Commission, Ghana. The maximum likelihood estimation (MLE) principle was adopted in fitting the DGP to yearly and aggregated data. The estimation involved two steps. First, we propose a modification to the μ and μ + 1 frequency method in the literature. The proposal provides an alternative routine for generating initial estimators for MLE, in cases of varied count intervals, as is a characteristic of the claim data under study. Second, a bootstrap algorithm is implemented to obtain standard errors of estimators of the DGP parameters. The performance of the DGP is compared to the negative binomial distribution in modelling the claim data using the Akaike and Bayesian information criteria. The results show that the DGP is appropriate for modelling the count of non-life insurance claims and provides a better fit to the regulatory claim data considered. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new three-parameter distribution defined on the unit interval. The density function of the distribution exhibits different kinds of shapes such as decreasing, increasing, left skewed, right skewed, and approximately symmetric. The failure rate function shows increasing, bathtub, and modified upside-down bathtub shapes. Six different frequentist estimation procedures were proposed for estimating the parameters of the distribution and their performance assessed via Monte Carlo simulations. Applications of the distribution were illustrated by analyzing two datasets and its fit compared to that of other distributions defined on the unit interval. Finally, we developed a regression model for a response variable that follows the new distribution. [ABSTRACT FROM AUTHOR]

Radon is one of the precursory phenomena that exist in connection to the occurrence of earthquakes and may have potential in forecasting these hazards. The data set in this study contains the observations of radon from August 01, 2014, to January 31, 2015, collected in Sobra city, northern Pakistan. Weibull, gamma, log-normal, log-logistic, and Pareto probability distribution were fitted over the radon on its original scale and a log scale. Log-logistic best fits the radon on both scales. The Tukey control charts reveal several anomalies that were compared with earthquake occurrence. There are five earthquakes that occurred during the same period as the radon monitoring program, having magnitude ranges between 4.9 and 5.5, with the ratio between strain radius and distance to the epicenter greater than or equal to 1. The results of this study demonstrate that, for earthquakes, seismic events show a correlation with increasing concentrations of radon gas before their occurrence. [ABSTRACT FROM AUTHOR]

For long-span cable-stayed bridges, cables serve as one of the most important components to guarantee structural integrity. Forces of stay cables indicate not only the performance of cables themselves but also the overall condition of bridges. In order to help stakeholders to make maintenance decisions, an extreme cable force estimation method was proposed based on cable force measurements and traffic data from the weighing system. First, raw monitoring data were preprocessed based on a median filtering to obtain usable cable force signals. The multiresolution wavelet method was used to extract traffic-induced force component from mixed signals. Then, a Monte Carlo-based random vehicle model was developed using traffic data from the weighing system. Based on field temperature measurements and simulation of traffic-induced effects, extreme cable forces with respect to vehicle loads and temperature effects were predicted by extreme value theory. The Generalized Pareto Distribution (GPD) was adopted to establish the probability distribution models of the daily maximum cable force. Then, the extreme value within a return period of 100 years was determined and compared with the design loading demand. Finally, the effectiveness of the proposed method was validated through a cable-stayed bridge in China. As a result, the low-frequency varying component of cable force response had positive correlation with environmental temperatures, and the extreme value of the predicted cable force under prospective traffic volumes was within limit interval value according to the design code. The conclusions can be utilized by bridge owners to make maintenance decisions. [ABSTRACT FROM AUTHOR]

Statistical distributions play a prominent role for modeling data in applied fields, particularly in actuarial, financial sciences, and risk management fields. Among the statistical distributions, the heavy-tailed distributions have proven the best choice to use for modeling heavy-tailed financial data. The actuaries are often in search of such types of distributions to provide the best description of the actuarial and financial data. This study presents a new power transformation to introduce a new family of heavy-tailed distributions useful for modeling heavy-tailed financial data. A submodel, namely, heavy-tailed beta-power transformed Weibull model is considered to demonstrate the adequacy of the proposed method. Some actuarial measures such as value at risk, tail value at risk, tail variance, and tail variance premium are calculated. A brief simulation study based on these measures is provided. Finally, an application to the insurance loss dataset is analyzed, which revealed that the proposed distribution is a superior model among the competitors and could potentially be very adequate in describing and modeling actuarial and financial data. [ABSTRACT FROM AUTHOR]

The Pareto model, first used in socioeconomic problems, has successfully been applied in many other areas such as astronomy, biology, bibliometrics, demography, insurance, or risk management. Although there are several variants of this distribution, the current study focuses on the classic Pareto distribution, also known as the Pareto type I distribution. We propose a new class of estimators for the Pareto shape parameter, obtained through a modification of the probability weighted moment method, called the log generalized probability weighted moments method. In addition to the asymptotic distribution, Monte Carlo simulations were performed to analyze the finite sample behavior of the proposed new estimators. A comparison with the most used estimators, such as the moment, the maximum likelihood, the least squares, and the probability weighted moments estimators was also performed. In addition, the estimators were used to construct asymptotic confidence intervals. To illustrate an application of the different estimation methods to a real data set from a clinical trial complete the article. Results indicate an overall good performance of the new proposed class. [ABSTRACT FROM AUTHOR]

We suppose that a product's lifetime follow the exponentiated Fréchet distribution of defined shape parameters. Based on this assumption, a double-acceptance sampling plan is constructed. The zero and one failure framework is essentially thought of: if no errors are found from the first sample, then the lot is approved; also, if at least two failures occur, it is rejected. In the first sample, if one failure is observed, then the second sample is taken and decided for the same length as the first one. The cumulative sample sizes of the first and second samples are determined on the basis of the stated confidence level of the consumer to ensure that the actual median is longer than the given life. As indicated by the various ratios of the actual median life to specified median lifetime, the operating characteristics are calculated and placed in presented tables. To decrease the risk of the producer at the predefined level, the minimum ratios of this sort are additionally obtained. Lastly, examples are provided for representation reasons for the proposed model. [ABSTRACT FROM AUTHOR]

Reinsurance plays a role of a stabilizer of the insurance industry and can be an effective tool to reduce the risk for the insurer. This paper aims to provide the optimal reinsurance design associated with the stop-loss reinsurance under the criterion of value-at-risk (VaR) risk measure. In this paper, the probability levels in the VaRs used by the both reinsurance parties are assumed to be different and the optimality results of reinsurance are derived by minimizing linear combination of the VaRs of the cedent and the reinsurer. The optimal parameter values of the stop-loss reinsurance policy are formally derived under the expectation premium principle. [ABSTRACT FROM AUTHOR]

This paper presents an effective approach for robust design optimization of car-door structures with spatially varied material properties. This spatially varied material property causes structural response quantities; for example, the natural frequency and the lateral stiffness coefficient become random variables. In this regard, the Karhunen-Loève expansion is first used to represent the elastic modulus and the mass density random fields as a series of random variables. Then, a stochastic finite-element model is formulated for uncertainty quantification of the car-door structure. Combined with a polynomial-based response surface model to mimic the true performance indicator, this allows one to efficiently evaluate probability constraints for the robust design optimization of the uncertain car-door structure. In numerical simulations, design variables of the uncertain car-door structure are defined as thickness values of the tailor rolled blank structure at various regions, whereas multiple design objectives are formulated via the structural weight, the first-order natural frequency, and the lateral stiffness coefficient. Results have shown that the mean value of performance indicators can be generally improved, whereas the response variance is further minimized to archive the robust design objective. The probability-based constraint is significant to relate the Pareto optimum set to the targeted structural safety level. The proposed approach is simple, suggesting an attractive tool for the robust design optimization of car-door structures with spatially varied material uncertainties. [ABSTRACT FROM AUTHOR]

Aiming at the important research topic of optimal scheduling in the microgrid field, the general model for multiobjective dynamic optimal scheduling of a microgrid is established with the objective of minimizing economic and environmental costs. On this basis, the model is organically integrated with constraint handling technology, multiobjective optimization, and biogeography-based optimization algorithm, and then a constrained multiobjective evolutionary model suitable for biogeography-based optimization is further established. The corresponding constraint handling mechanism, the determination method of habitat suitability index, and migration strategy are improved, and the convergence performance and the distribution uniformity of Pareto frontier for multiobjective evolutionary algorithm are effectively enhanced. Applied to the optimal scheduling of typical microgrid systems, the effectiveness of the proposed model and method is verified. [ABSTRACT FROM AUTHOR]

In this paper, a new definition of the number of observations near the k th order statistics is developed. Then some characterization results for Pareto and some related distributions are established in terms of mass probability function, first moment of these new counting random variables, and using completeness properties of the sequence of functions x n , 0 < x < 1 , n ≥ 1 . Finally, new goodness-of-fit tests based on these new characterizations for Pareto distribution are presented. And the power values of the proposed tests are compared with the power values of well-known tests such as Kolmogorov–Smirnov and Cramer-von Mises tests by Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

In many practical situations the decision-maker has to pay special attention to decision space to determine the constructability of a potential solution, in addition to its optimality in objective space. Practically desirable solutions are those around preferred values in decision space and within a distance from optimality. This work investigates two methods to find simultaneously optimal and practically desirable solutions. The methods expand the objective space by adding fitness functions that favor preferred values for some variables. In addition, the methods incorporate a ranking mechanism that takes into account Pareto dominance in objective space and desirability in decision space. One method searches with one population in the expanded space, whereas the other one uses two populations to search concurrently in the original and expanded space. Our experimental results on benchmark and real world problems show that the proposed method can effectively find optimal and practically desirable solutions. [ABSTRACT FROM AUTHOR]

The frequency and severity of climate abnormal change displays an irregular upward cycle as global warming intensifies. Therefore, this paper employs a doubly stochastic Poisson process with Black Derman Toy (BDT) intensity to describe the catastrophic characteristics. By using the Property Claim Services (PCS) loss index data from 2001 to 2010 provided by the US Insurance Services Office (ISO), the empirical result reveals that the BDT arrival rate process is superior to the nonhomogeneous Poisson and lognormal intensity process due to its smaller RMSE, MAE, MRPE, and U and larger E and d. Secondly, to depict extreme features of catastrophic risks, this paper adopts the Peak Over Threshold (POT) in extreme value theory (EVT) to characterize the tail characteristics of catastrophic loss distribution. And then the loss distribution is analyzed and assessed using a quantile-quantile (QQ) plot to visually check whether the PCS index observations meet the generalized Pareto distribution (GPD) assumption. Furthermore, this paper derives a pricing formula for zero-coupon catastrophe bonds with a stochastic interest rate environment and aggregate losses generated by a compound doubly stochastic Poisson process under the forward measure. Finally, simulation results verify pricing model predictions and show how catastrophic risks and interest rate risk affect the prices of zero-coupon catastrophe bonds. [ABSTRACT FROM AUTHOR]

A robust mean variance optimization model is set up for an economic dispatch problem integrating uncertain wind power in a real-time electricity market. The objective of the model is to find a robust optimal solution so as to minimize both the expected total generation cost and hedge the risk resulting from the robustness. Furthermore, the proposed model is transformed into a biobjective second-order cone programming. To generate an evenly distributed Pareto front set that will not overrepresent one region of the design space or neglect others, we propose a normalized-constraint method in this work. The Pareto front, demonstrated in the Institute of Electrical and Electronics Engineers 118-bus case study, shows a trade-off between total generation cost and risk. An important observation during the case study is that the Pareto front of the robust mean variance model has a special shape that, by sacrificing only a little total generation cost, can greatly reduce the risk in the robust real-time economic dispatch. [ABSTRACT FROM AUTHOR]

This paper deals with the Bayesian inference on step-stress partially accelerated life tests using Type II progressive censored data in the presence of competing failure causes. Suppose that the occurrence time of the failure cause follows Pareto distribution under use stress levels. Based on the tampered failure rate model, the objective Bayesian estimates, Bayesian estimates, and E-Bayesian estimates of the unknown parameters and acceleration factor are obtained under the squared loss function. To evaluate the performance of the obtained estimates, the average relative errors (AREs) and mean squared errors (MSEs) are calculated. In addition, the comparisons of the three estimates of unknown parameters and acceleration factor for different sample sizes and different progressive censoring schemes are conducted through Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

A geological anomaly is the basis of mineral deposit prediction. Through the study of the knowledge and characteristics of geological anomalies, the category of extreme value theory (EVT) to which a geological anomaly belongs can be determined. Associating the principle of the EVT and ensuring the methods of the shape parameter and scale parameter for the generalized Pareto distribution (GPD), the methods to select the threshold of the GPD can be studied. This paper designs a new algorithm called the EVT model of geological anomaly. These study data on Cu and Au originate from 26 exploration lines of the Jiguanzui Cu-Au mining area in Hubei, China. The proposed EVT model of the geological anomaly is applied to identify anomalies in the Jiguanzui Cu-Au mining area. The results show that the model can effectively identify the geological anomaly region of Cu and Au. The anomaly region of Cu and Au is consistent with the range of ore bodies of actual engineering exploration. Therefore, the EVT model of the geological anomaly can effectively identify anomalies, and it has a high indicating function with respect to ore prospecting. [ABSTRACT FROM AUTHOR]

The bit error probability (BEP) for many wireless communications networks can be expressed in the form R = Pr (X2 < X1) where X1 and X2 are independent random variables. Here, a comprehensive collection of formulas is derived for R by assuming the most commonly known models for X1 and X2. A discussion is provided of four possible applications to problems in wireless communications. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]