Applications of Bootstrap in Analyzing General Extreme Value Distributions

The bootstrap method is one of the new ways of studying statistical math which this article uses but is a major tool for studying and evaluating the values of parameters in probability distribution.Our research is concerned overview of the theory of infinite distribution functions.The tool to deal with the problems raised in the paper is the mathematical methods of random analysis(theory of random process and multivariate statistics).In this article,we introduce the new function to find out the bias and standard error with jackknife method for Generalized Extreme Value distributions.

Analyzing the Annual Maximum Magnitude of Earthquakes in Japan by Extreme Value Theory

One of the most important and interesting issues associated with the earthquakes is the long-term trend of the extreme events. Extreme value theory provides methods for analysis of the most extreme parts of data. We estimated the annual maximum magnitude of earthquakes in Japan by extreme value theory using earthquake data between 1900 and 2019. Generalized extreme value (GEV) distribution was applied to fit the extreme indices. The distribution was used to estimate the probability of extreme values in specified time periods. The various diagnostic plots for assessing the accuracy of the GEV model fitted to the magnitude of maximum earthquakes data in Japan gave the validity of the GEV model. The extreme value index, ξ was evaluated as −0.163, with a 95% confidence interval of [−0.260, −0.0174] by the use of profile likelihood. Hence, the annual maximum magnitude of earthquakes has a finite upper limit. We obtained the maximum return level for the return periods of 10, 20, 50, 100 and 500 years along with their respective 95% confidence interval. Further, to get a more accurate confidence interval, we estimated the profile log-likelihood. The return level estimate was obtained as 7.83, 8.60 and 8.99, with a 95% confidence interval of [7.67, 8.06], [8.32, 9.21] and [8.61, 10.0] for the 10-, 100- and 500-year return periods, respectively. Hence, the 2011 off the Pacific coast of Tohoku Earthquake, which was the largest in the observation history of Japan, had a magnitude of 9.0, and it was a phenomenon that occurs once every 500 year.

Empirical Analysis of Value-at-Risk Estimation Methods Using Extreme Value Theory

This paper investigates methods of value-at-risk (VaR) estimation using extreme value theory (EVT). It compares two different estimation methods, 'two-step subsample bootstrap' based on moment estimation and maximum likelihood estimation (MLE), according to their theoretical bases and computation procedures. Then, the estimation results are analyzed together with those of normal method and empirical method. The empirical research of foreign exchange data shows that the EVT methods have good characters in estimating VaR under extreme conditions and 'two-step subsample bootstrap' method is preferable to MLE.

Red Tide Frequency Analysis Using the Extreme Value Theory

In recent years, the red tide erupted frequently, and caused a great economic loss. At present, most literatures emphasize the academic research on the growth mechanism of red tide alga. In order to find out the characters of red tide in detail and improve the precision of forecast, this paper gives some new approaches to dealing with the red tide. By the extreme values, we deal with the red tide frequency analysis and get the estimation of T-times red tide level U (T), which is the level once the consistence of red tide alga exceeds on the average in a period of T times.

Assesment of Frequency-Magnitude of Extreme Rainfall Events-Case Study of the MeKong River Delta

Extreme rainfall events are primary natural hazards, which cause a severe threat to people and their properties in populated cities, which are normally located in coastal areas in Vietnam. Analysing these events by using a data series observed over years will support us to draw a picture of how the climate change impact on local environments. The purpose of this report is to understand the characteristics of the extreme rainfall events in MEKONG river delta （south VietNam）. Daily rainfall data in the period of 30 years for a meteorological station in each area were collected from the Vietnam National Hydro-meteorological Service. The extreme rainfall events were defined as those exceeding the 95th percentile for each station. The analytical results show that the rainfall values （95th percentile） are 37.4 mm/day at Nam Can station, 27 mm/day at My Thanh station, 22.4 mm/day at Hoa Binh station, 23.8 mm/day at Binh Dai station and 22.7 mm/day at Ben Trai station. The highest rainfall data ever recorded are 246.4 mm/day （Nam Can）, 174.5 mm/day （My Thanh）, 179 mm/day （Hoa Bin_h）, 187.3 mm/day （Binh Dai） and 136.3 mm/day （Ben Trai） during 1983-2012. The result of the Mann-Kendall tests show that there was a significant creasing of the rainfall at Nam Can, My Thanh station in two periods （1983-2012, 1998-2012） while no clear trend of the rainfall was recoreded at Hoa Birth, Binh Dai, Ben Trai station. In order to estimate the return period of the extreme rainfall events, the method General Extreme Value Distribution was used to calculate frequent distribution. The magnitudes of daily maximum rainfall were from 2 to 100 years. The results of return period show that maximum rainfalls are 46.6 mm at Nam Can station （highest） and 31.4 mm at Hoa Birth station （lowest） during 50 years. Similarly, maximum rainfalls are expected to be about 55.1 mm at Nam Can station and 37.2 mm at Hoa Birth station for 100 years.

Spatial Modeling of the Highest Daily Maximum Temperature in Korea via Max-stable Processes

This paper examines the annual highest daily maximum temperature （DMT） in Korea by using data from 56 weather stations and employing spatial extreme modeling. Our approach is based on max-stable processes （MSP） with Schlather＇s characterization. We divide the country into four regions for a better model fit and identify the best model for each region. We show that regional MSP modeling is more suitable than MSP modeling for the entire region and the pointwise generalized extreme value distribution approach. The advantage of spatial extreme modeling is that more precise and robust return levels and some indices of the highest temperatures can be obtained for observation stations and for locations with no observed data, and so help to determine the effects and assessment of vulnerability as well as to downscale extreme events.

Local and regional flood frequency analysis based on hierarchical Bayesian model in Dongting Lake Basin,China

This study developed a hierarchical Bayesian(HB)model for local and regional flood frequency analysis in the Dongting Lake Basin,in China.The annual maximum daily flows from 15 streamflow-gauged sites in the study area were analyzed with the HB model.The generalized extreme value(GEV)distribution was selected as the extreme flood distribution,and the GEV distribution location and scale parameters were spatially modeled through a regression approach with the drainage area as a covariate.The Markov chain Monte Carlo(MCMC)method with Gibbs sampling was employed to calculate the posterior distribution in the HB model.The results showed that the proposed HB model provided satisfactory Bayesian credible intervals for flood quantiles,while the traditional delta method could not provide reliable uncertainty estimations for large flood quantiles,due to the fact that the lower confidence bounds tended to decrease as the return periods increased.Furthermore,the HB model for regional analysis allowed for a reduction in the value of some restrictive assumptions in the traditional index flood method,such as the homogeneity region assumption and the scale invariance assumption.The HB model can also provide an uncertainty band of flood quantile prediction at a poorly gauged or ungauged site,but the index flood method with L-moments does not demonstrate this uncertainty directly.Therefore,the HB model is an effective method of implementing the flexible local and regional frequency analysis scheme,and of quantifying the associated predictive uncertainty.

Influence of changes in extreme daily rainfall distribution on the stability of residual soil slopes

Many landslides triggered by intense rainfall have occurred in moun-tainous areas in Thailand,causing major economic losses and infra-structure damage.Extreme daily rainfall is a significant trigger for hillslope instability.Increases in extreme daily rainfall intensity due to climate change may be one of the key factors responsible for the increased landslides.Thus,in this context,changes in the intensity of extreme daily rainfall in Chiang Mai Province in North Thailand and their effects on hillslope stability are analyzed.Extreme rainfall is modeled using a generalized extreme value distribution and esti-mated for various return periods.A numerical analysis of seepage and an infinite slope stability model are combined to understand the hillslope response under extreme rainfall conditions.The analysis period is divided into two periods of 34 years:1952 to 1985 and 1986 to 2019.According to the analysis results,the distribution of extreme daily rainfall changes in terms of location.The average annual daily maximum rainfall increased by approximately 11.13%.The maximum decrease in the safety factor is approximately 4.5%;therefore,these changes in extreme daily rainfall should be consid-ered in future landslide prevention policies.

Confirmation of the Record of the Serpent Eel, Ophisurus serpens （Family： Ophichthidae） from Mersin Bay （NE Mediterranean, Turkey）

A specimen of the serpent eel, Ophisurus serpens, with a total length of 190.2 cm was caught off the coast of Mersin （Incekum）, Turkey on November 2014 during trawling. This manuscript presents the first digitized specimen of O. serpens from the Mersin Bay （northeastern Mediterranean）, and hence, confirms the presence of the species in the northeastern Mediterranean despite a suspicious previous report, possibly mistaken with Echelus myrus, of the species from Yumurtahk Bay. Remarks on the morphology and geographical distribution of the species in the Mediterranean Sea, Turkey are given.

How Frequently Will the Persistent Heavy Rainfall over the Middle and Lower Yangtze River Basin in Summer 2020 Happen under Global Warming?

The middle and lower Yangtze River basin(MLYRB)suffered persistent heavy rainfall in summer 2020,with nearly continuous rainfall for about six consecutive weeks.How the likelihood of persistent heavy rainfall resembling that which occurred over the MLYRB in summer 2020(hereafter 2020PHR-like event)would change under global warming is investigated.An index that reflects maximum accumulated precipitation during a consecutive five-week period in summer(Rx35day)is introduced.This accumulated precipitation index in summer 2020 is 60%stronger than the climatology,and a statistical analysis further shows that the 2020 event is a 1-in-70-year event.The model projection results derived from the 50-member ensemble of CanESM2 and the multimodel ensemble(MME)of the CMIP5 and CMIP6 models show that the occurrence probability of the 2020PHR-like event will dramatically increase under global warming.Based on the Kolmogorov-Smirnoff test,one-third of the CMIP5 and CMIP6 models that have reasonable performance in reproducing the 2020PHR-like event in their historical simulations are selected for the future projection study.The CMIP5 and CMIP6 MME results show that the occurrence probability of the 2020PHR-like event under the present-day climate will be double under lower-emission scenarios(CMIP5 RCP4.5,CMIP6 SSP1-2.6,and SSP2-4.5)and 3-5 times greater under higher-emission scenarios(3.0 times for CMIP5 RCP8.5,2.9 times for CMIP6 SSP3-7.0,and 4.8 times for CMIP6 SSP5-8.5).The inter-model spread of the probability change is small,lending confidence to the projection results.The results provide a scientific reference for mitigation of and adaptation to future climate change.

Parametric and Non-Parametric Survival Analysis of Patients with Acute Myeloid Leukemia (AML)

Background: Acute Myeloid leukemia (AML) is the most prominent acute leukemia in adults. In the United States, we experience over 20,000 cases per year. Over the past decade, improvements in the diagnosis of subtypes of AML and advances in therapeutic approaches have improved the outlook for patients with AML. However, despite these advancements, the survival rate among patients who are less than 65 years of age is only 40 percent. Purpose: The purpose of the paper is to study if there exists any significant difference in the survival probabilities of male and female AML patients. Also, we want to investigate if there is any parametric probability distribution that best fits the male and female patient survival and compare the survival probabilities with the non-parametric Kaplan-Meier (KM) method. Methods: We used both parametric and non-parametric statistical methods to perform the survival analysis to assess the survival probabilities of 2015 patients diagnosed with AML. Results: We found evidence of a statistically significant difference between the mean survival time of male and female patients diagnosed with AML. We performed parametric survival analysis and found a Generalized Extreme Value (GEV) distribution best fitting the data of the survival time for male and female patients. We then estimated the survival probabilities and compared them with the frequently used non-parametric Kaplan-Meier (KM) survival method. Conclusion: The comparison between the survival probability estimates of the two methods revealed a better survival probability estimate by the parametric method than the Kaplan-Meier. We also compared the median survival time of male and female patients individually with descriptive, parametric, and non-parametric methods of analysis. The parametric survival analysis is more robust and efficient because it is based on a well-defined parametric probabilistic distribution, hence preferred over the non-parametric Kaplan-Meier estimate. This study offers therapeutic significance for further enhancement to treat patients with Acute Myeloid Leukemia.