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

The probability characteristics of the heliostat support column base shear are discussed, and related methods are used to determine whether the base shear is conformed to the Gaussian distribution under all working conditions. Then, three kinds of peak estimating methods are selected to calculate the peak base shear, and results are compared. It is found that the Generalized Pareto Distribution (GPD) method is the most suitable for calculating the peak value of the heliostat support column base shear. Finally, the variation law of peak values of heliostat support column base shear is obtained and the variation law of peak and mean base shear are compared. The judgment criterion of whether the heliostat support column base shear is conformed to the Gaussian distribution is obtained, Gaussian and Non-Gaussian regions are divided. The peak value of the heliostat support column base shear which is calculated by the GPD method and met the specified guarantee rate has high accuracy. It can be met the needs of engineering application. The analysis of the variation law of peak values of heliostat support column base shear can be a reference for engineering design and scientific research. • Study of probability characteristics of heliostat base shear is provided. • The criterion of whether the base shear is conformed to the Gaussian distribution. • GPD method is the most suitable method for calculating peak base shear of heliostat. • Positive and negative maximum peak base shear should be studied in design. [ABSTRACT FROM AUTHOR]

The development and application of the Envelope Peak-over-Threshold (EPOT) method is summarized for the roll motion of a ship in irregular waves. The method is based on the conventional Peak-over-Threshold (POT) method, but uses an envelope of the peaks for declustering the data. As suggested by a reduced-order model, a power-law tail should be applicable for the peaks of roll motions, which allows the introduction of physical considerations into the statistical model. A data-driven Generalized Pareto distribution (GPD) is applied to study the behavior of the shape parameter on large-volume samples in order to confirm the theoretical prediction of the tail structure. The physics-informed statistical model approximates data above a suitable threshold with a Pareto distribution, while the threshold is determined with a prediction error criterion. An example is included, where extrapolations with GPD are compared to the physics-informed model. • Application of Peak-over-Threshold method is considered where a time history envelope is used for declustering the data. • The study of behavior of distribution tails of roll motion peaks. • A physics-informed model with power-law, Pareto tail was formulated and applied to amplitudes of roll motions. [ABSTRACT FROM AUTHOR]

Estimation of quantiles of Annual Maximum Wind Speed (AMWS) is needed in different environmental fields, engineering risk analysis, design of structures, renewable energy sources, agricultural operations, and climatology. Therefore, wind speed frequency analysis (WSFA) was carried out at nine stations from Pakistan. Multiparameter Probability Distributions (PDs), such as Generalized logistic (GLO), Generalized Extreme Value (GEV), Generalized Normal (GNO), Generalized Pareto (GPA), Weibull (WEI), Pearson type 3 (P3), Log Pearson type 3 (LP3); and two parameter PDs, such as Logistic (LOG), Normal (NOR), Gumbel (GUM), Exponential (EXP), and Uniform (UNI) were used to determine the most suitable distributions for the nine stations. The method of L-moments was used for estimating parameters of the distributions. The Kolmogorov-Smirnov (KS) test, Anderson-Darling (AD) test, Minimum L-Kurtosis (ML-K) Difference Criterion, and L-moment ratio diagram (L-ratio diagram) showed that four distributions, namely GEV, GNO, GPA, and GLO were the most suitable distributions for different stations and were superior to the two-parameter distributions. The quantile estimates (design estimates) from multiparameter PDs provide information on how fast the maximum wind will pass through a certain place and hence are important for policy makers and planners in the design and construction of different structures. The Multivariate Diebold–Mariano (DM) test was applied to check the accuracy of design estimates from the best fitted PDs and results indicated that they were significantly different. • Identification and evaluation of the best model among different Probability distributions for Annual Maximum Wind Speed. • Evaluation of the resulting quantiles through relative absolute error measurement. • Evaluation of relative absolute error from different Probability distributions through Multivariate Diebold–Mariano test. • Identification of the stations likely to face maximum or minimum wind speed in the future. [ABSTRACT FROM AUTHOR]

Abstract In this study, a robust semi-parametric approach which involves combining the empirical distribution and Pareto model is applied for measuring the income distribution in Malaysia based on the survey data of household incomes for the years of 2007, 2009, 2012 and 2014. From our analysis, it is found that the Pareto model is well fitted to the top household incomes for all years considered, suggesting that this model is a suitable parametric distribution to describe the top household incomes in Malaysia. Based on the semi-parametric Gini, generalized entropy and Atkinson indices, it is found that the income inequality shows a decreasing trend over the period, indicating an improvement of income distribution in Malaysia. Moreover, the fitted semi-parametric Lorenz curves show that the economic pie of the high income group reduced slightly after being taken up by the low income group while there is no clear change for the middle household income group. Highlights • A robust semi-parametric approach provides good results for measuring income inequality. • PITSE method provides good parameter estimation of Pareto model in the presence of outliers. • Various inequality indices based on semi-parametric model are provided. [ABSTRACT FROM AUTHOR]

An energy-harvesting suspension system of a vehile can improve both the ride comfort and fuel efficiency. However, such a suspension design is a multi-parameter and multi-objective optimization problem. To solve this problem, the sensitivities of performance criteria to the parameters of an energy-harvesting suspension are studied firstly, with analytical solutions and numerical solutions of the root mean squares of the design criteria. To get a trade-off between the conflicting performance indexes of the suspension, a non-dimensional mixed index based on safety probability is proposed to evaluate the performance, where the ride comfort probability and handling stability probability are adopted to unify the dimensions. On this basis, the genetic algorithm is adopted to solve the multi-parameter optimization problem. Numerical analysis and experiments are conducted to verify the performance of the optimized energy-harvesting suspension system. Results show that ride comfort and handling stability are two conflicting performance indexes, and only a Pareto optimal result can be obtained by multi-objective optimization algorithm. With the proposed mixed index of suspension as the optimal object, the ride comfort can be improved significantly, while the handling stability is ensured. Additionally, for a given energy-harvesting suspension, by merely optimizing the damping coefficient, the suspension performance can be improved with variations of road conditions, which illustrates the potential good performance of the energy-harvesting suspension. • A non-dimensional mixed index based on safety probability is proposed. • The inerter is fully considered in the suspension modeling and operation. • The sensitivity of performance criteria to the parameters is studied. • The damping coefficient is optimized at different road levels. • The safety probability based optimization is analyzed verified. [ABSTRACT FROM AUTHOR]

Strongly positive sea-surface temperature anomalies developed in the Northeast Pacific Ocean during the winter of 2013/14. Sea-surface temperature anomalies near Station Papa, in the Gulf of Alaska, were more than 4.5 standard deviations above normal. Temperature anomalies in excess of 4 standard deviations were still present subsurface into 2017. Such departures from climatology raises this event from unusual to extraordinary. On the principle that an extraordinary observation needs extraordinary proof, in this paper we examine three datasets that are completely independent of each other and examine how closely those datasets correspond with each other. The correspondence is found to be close. We also discuss the statistical interpretation and probability that a 4.5σ departure from normal can occur. • In 2014 anomalies were seen in the Gulf of Alaska exceeding 4½ standard deviations - an unusual observation that needs verification. • The existence of these large anomalies is verified using 3 non-overlapping data sets. • Gaussian and Pareto probability distributions are used to estimate the return times for these anomalies. [ABSTRACT FROM AUTHOR]