GENERALIZED PARETO DISTRIBUTION FIT TO MEDICAL INSURANCE CLAIMS DATA

How to choose an optimal threshold is a key problem in the generalized Pareto distribution （GPD） model. This paper attains the exact threshold by testing for GPD,and shows that GPD model allows the actuary to easily estimate high quantiles and the probable maximum loss from the medical insurance claims data.

Generalized Pareto Distribution Model and Its Application to Hydrocarbon Resource Structure Prediction of the Huanghua Depression

The generalized Pareto distribution model is a kind of hydrocarbon pool size probability statistical method for resource assessment. By introducing the time variable, resource conversion rate and the geological variable, resource density, such model can describe not only different types of basins, but also any exploration samples at different phases of exploration, up to the parent population. It is a dynamic distribution model with profound geological significance and wide applicability. Its basic principle and the process of resource assessment are described in this paper. The petroleum accumulation system is an appropriate assessment unit for such method. The hydrocarbon resource structure of the Huanghua Depression in Bohai Bay Basin was predicted by using this model. The prediction results accord with the knowledge of exploration in the Huanghua Depression, and point out the remaining resources potential and structure of different petroleum accumulation systems, which are of great significance for guiding future exploration in the Huanghua Depression.

Prediction of Short-Term Distributions of Load Extremes of Offshore Wind Turbines

This paper proposes a new methodology to select an optimal threshold level to be used in the peak over threshold （POT） method for the prediction of short-term distributions of load extremes of offshore wind turbines. Such an optimal threshold level is found based on the estimation of the variance-to-mean ratio for the occurrence of peak values, which characterizes the Poisson assumption. A generalized Pareto distribution is then fitted to the extracted peaks over the optimal threshold level and the distribution parameters are estimated by the method of the maximum spacing estimation. This methodology is applied to estimate the short-term distributions of load extremes of the blade bending moment and the tower base bending moment at the mudline of a monopile-supported 5MW offshore wind turbine as an example. The accuracy of the POT method using the optimal threshold level is shown to be better, in terms of the distribution fitting, than that of the POT methods using empirical threshold levels. The comparisons among the short-term extreme response values predicted by using the POT method with the optimal threshold levels and with the empirical threshold levels and by using direct simulation results further substantiate the validity of the proposed new methodology.

A Newly-Discovered GPD-GEV Relationship Together with Comparing Their Models of Extreme Precipitation in Summer

It has been theoretically proven that at a high threshold an approximate expression for a quantile of GEV （Generalized Extreme Values） distribution can be derived from GPD （Generalized Pareto Distribution）. Afterwards, a quantile of extreme rainfall events in a certain return period is found using L-moment estimation and extreme rainfall events simulated by GPD and GEV, with all aspects of their results compared. Numerical simulations show that POT （Peaks Over Threshold）-based GPD is advantageous in its simple operation and subjected to practically no effect of the sample size of the primitive series, producing steady high-precision fittings in the whole field of values （including the high-end heavy tailed）. In comparison, BM （Block Maximum）-based GEV is limited, to some extent, to the probability and quantile simulation, thereby showing that GPD is an extension of GEV, the former being of greater utility and higher significance to climate research compared to the latter.

Peaks over Manifold (POM): A Novel Technique to Analyze Extreme Events over Surfaces

We present a novel method to analyze extreme events of flows over manifolds called Peaks Over Manifold (POM). Here we show that under general and realistic hypotheses, the distribution of affectation measures converges to a Generalized Pareto Distribution (GPD). The method is applicable to floods, ice cover extent, extreme rainfall or marine heatwaves. We present an application to a synthetic data set on tide height and to real ice cover data in Antartica.

Consistency of the <i>φ</i>-Divergence Based Change Point Estimator

This paper utilizes a change-point estimator based on the φ-divergence. Since we seek a near perfect translation to reality, then locations of parameter change within a finite set of data have to be accounted for since the assumption of stationary model is too restrictive especially for long time series. The estimator is shown to be consistent through asymptotic theory and finally proven through simulations. The estimator is applied to the generalized Pareto distribution to estimate changes in the scale and shape parameters.

Gigacycle Fatigue Behavior of 1800 MPa Grade High Strength Spring Steel for Automobile Lightweight

Gigacycle fatigue behavior of 60Si2CrVA high strength spring steel was investigated by ultrasonic fatigue test machine. Fatigue fractography was observed by scanning electron microscopy （SEM）. Maximum inclusion sizes and fatigue strength in different volumes were estimated by statistics of extreme values （SEV） and generalized Pareto distribution （GPD） methods. The results showed that S N curves of 60Si2CrVA spring steels for two rolling processes were not horizontal asymptotes but a gradient in a regime of 109 cycles, and traditional fatigue limits were eliminated. Surface machined topography and inclusions in steel were major factors that led to elimination of fatigue limit for 60Si2CrVA spring steel. The SEV and GPD methods could effectively predict size of the maximum inclusion and fatigue strength in different volumes of 60Si2CrVA spring steel. Predicted fatigue strength was in accordance with experimental results by ultrasonic fatigue testing.

Experimental Simulations of Extreme Precipitation Based on the Multi-Status Markov Chain Model

A multi-status Markov chain model is proposed to produce daily rainfall, and based on which extreme rainfall is simulated with the generalized Pareto distribution （GPD）. The simulated daily rainfall shows high precision at most stations, especially in pluvial regions of East China. The analysis reveals that the multi- status Markov chain model excels the bi-status Markov chain model in simulating climatic features of extreme rainfall. Results from the selected six stations demonstrate excellent simulations in the following aspects： standard deviation of monthly precipitation, daily maximum precipitation, the monthly mean rainfall days, standard deviation of daily precipitation and mean daily precipitation, which are proved to be consistent with the observations. A comparative study involving 78 stations in East China also reveals good consistency in monthly mean rainfall days and mean daily maximum rainfall, except mean daily rainfall. Simulation results at the above 6 stations have shown satisfactory fitting capability of the extreme precipitation GPD method. Good analogy is also found between simulation and observation in threshold and return values. As the errors of the threshold decrease, so do the differences between the return and real values. All the above demonstrates the applicability of the Markov chain model to extreme rainfall simulations.

Tail risks and infectious disease: Influenza mortality in the U.S., 1900-2018

I use extreme values theory and data on influenza mortality from the U.S.for 1900 to 2018 to estimate the tail risks of mortality.I find that the distribution for influenza mortality rates is heavy-tailed,which suggests that the tails of the mortality distribution are more informative than the events of high frequency(i.e.,years of low mortality).I also discuss the implications of my estimates for risk management and pandemic planning.