A Comparison of Four Methods of Estimating the Scale Parameter for the Exponential Distribution

In this paper, the estimators of the scale parameter of the exponential distribution obtained by applying four methods, using complete data, are critically examined and compared. These methods are the Maximum Likelihood Estimator (MLE), the Square-Error Loss Function (BSE), the Entropy Loss Function (BEN) and the Composite LINEX Loss Function (BCL). The performance of these four methods was compared based on three criteria: the Mean Square Error (MSE), the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). Using Monte Carlo simulation based on relevant samples, the comparisons in this study suggest that the Bayesian method is better than the maximum likelihood estimator with respect to the estimation of the parameter that offers the smallest values of MSE, AIC, and BIC. Confidence intervals were then assessed to test the performance of the methods by comparing the 95% CI and average lengths (AL) for all estimation methods, showing that the Bayesian methods still offer the best performance in terms of generating the smallest ALs.

Current status of small yellow croaker resources in the southern Yellow Sea and the East China Sea

We used data from bottom trawl surveys to study the factors influencing the abundance of small yellow croaker, Larimichthys polyactis, in the southern Yellow Sea （SYS） and the East China Sea （ECS）. The resource density index （RD1） was generally higher in summer and autumn than in spring and winter. RDIs were also significantly greater in the SYS than in the ECS in summer and autumn. The bottom water salinity and depth of spatial distribution of small yellow croaker was similar between the two areas in summer, but different in other seasons. Regression analysis suggested that environmental factors such as bottom water temperature, salinity, and depth influenced the RDIs in summer in these areas. Growth condition factor （GCF） in the two areas varied monthly and the croaker in the SYS grew more slowly than those in the ECS. This was likely due to the low bottom temperature of the Yellow Sea Cold Water Mass in summer and autumn or to higher human fishing pressure in the ECS. To ensure sustainable utilization of the croaker stocks in these regions, we recommend reducing the fishing intensity, increasing the cod-end mesh size, and improving the protection of juveniles.

An improved joint method for onset picking of acoustic emission signals with noise

The onset times of acoustic signals with spikes,heavy bodies and unclear takeoffs are difficult to be picked accurately by the automatic method at present.To deal with this problem,an improved joint method based on the discrete wavelet transform(DWT),modified energy ratio(MER)and Akaike information criterion(AIC)pickers,has been proposed in this study.First,the DWT is used to decompose the signal into various components.Then,the joint application of MER and AIC pickers is carried out to pick the initial onset times of all selected components,where the minimum AIC position ahead of MER onset time is regarded as the initial onset time.Last,the average for initial onset times of all selected components is calculated as the final onset time of this signal.This improved joint method is tested and validated by the acoustic signals with different signal to noise ratios(SNRs)and waveforms.The results show that the improved joint method is not affected by the variations of SNR,and the onset times picked by this method are always accurate in different SNRs.Moreover,the onset times of all acoustic signals with spikes,heavy bodies and unclear takeoffs can be accurately picked by the improved joint method.Compared to some other methods including MER,AIC,DWT-MER and DWT-AIC,the improved joint method has better SNR stabilities and waveform adaptabilities.

On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting

This study investigates the volatility in daily stock returns for Total Nigeria Plc using nine variants of GARCH models:sGARCH,girGARCH,eGARCH,iGARCH,aGARCH,TGARCH,NGARCH,NAGARCH,and AVGARCH along with value at risk estimation and backtesting.We use daily data for Total Nigeria Plc returns for the period January 2,2001 to May 8,2017,and conclude that eGARCH and sGARCH perform better for normal innovations while NGARCH performs better for student t innovations.This investigation of the volatility,VaR,and backtesting of the daily stock price of Total Nigeria Plc is important as most previous studies covering the Nigerian stock market have not paid much attention to the application of backtesting as a primary approach.We found from the results of the estimations that the persistence of the GARCH models are stable except for few cases for which iGARCH and eGARCH were unstable.Additionally,for student t innovation,the sGARCH and girGARCH models failed to converge;the mean reverting number of days for returns differed from model to model.From the analysis of VaR and its backtesting,this study recommends shareholders and investors continue their business with Total Nigeria Plc because possible losses may be overcome in the future by improvements in stock prices.Furthermore,risk was reflected by significant up and down movement in the stock price at a 99%confidence level,suggesting that high risk brings a high return.

一项优化AJCC/UICC pTNM胃癌分期预后预测效能的多中心研究

背景与目的美国癌症联合会与国际抗癌联盟(AmericanJointCommitteeonCancer/UnionforInternationalCancerControl,A JCC/UICC)联合发布的第8版TNM病理分期(pathological tumor?node?metastasis,p TNM)较前进行了重要修改,以提高胃癌患者预后预测准确性。然而,该分期不同亚组间患者的预后仍存在一定的同质性。本研究旨在对比第8版和第7版AJCC/UICC pTNM分期对胃癌预后的预测效能,并纳入外部验证对现有分期进行优化。方法共纳入分析7911例就诊于中国3家大型医疗中心和10,208例美国流行病监测与最终治疗结果(Surveillance Epidemiology and End Results,SEER)数据库的患者临床资料。采用log-rank检验、线性趋势检验、似然比检验和赤池信息量准则(akaike information criterion,AIC)梯度评估第7、8版AJCC/UICC pTNM分期系统的同质性、辨别力和单调性,在此基础上优化分期并以SEER数据集作为外部验证。结果第7、8版分期系统在两组数据集中均存在明显分期偏移,且集中在III期患者。IIIA、IIIB和IIIC期各亚组内患者的生存率有显著差异,表明两个系统分期分层的同质性较差。我们根据中国患者数据构建一个新的改良版p TNM分期,上述分层同质性问题得到明显改善,进一步以SEER数据作为验证集同样得到了良好的结果。相较第7、8版分期系统,改良版p TNM分期在两组数据集中均有较高的log-rank、线性趋势、似然比卡方值和较低的AIC值,显示出更优的辨别力、同质性、单调性和预后预测效能。结论第8版AJCC/UICC pTNM分期系统优于第7版,但预后预测的同质性均较差。我们构建的改良版p TNM分期在两组大样本胃癌数据集中均显示出理想的分期分层和预后预测效能。

Proposal and validation of a modified staging system to improve the prognosis predictive performance of the 8th AJCC/ UICC pTNM staging system for gastric adenocarcinoma: a multicenter study with external validation

Background:The 8th edition of the American Joint Committee on Cancer/Union for International Cancer Control(AJCC/UICC)pathological tumor-node-metastasis(pTNM)staging system may have increased accuracy in predicting prognosis of gastric cancer due to its important modifications from previous editions.However,the homogeneity in prognosis within each subgroup classified according to the 8th edition may still exist.This study aimed to compare and analyze the prognosis prediction abilities of the 8th and 7th editions of AJCC/UICC pTNM staging system for gastric cancer and propose a modified pTNM staging system with external validation.Methods:In total,clinical data of 7911 patients from three high-capacity institutions in China and 10,208 cases from the Surveillance,Epidemiology,and End Results(SEER)Program Registry were analyzed.The homogeneity,discrimina-tory ability,and monotonicity of the gradient assessments of the 8th and 7th editions of AJCC/UICC pTNM staging system were compared using log-rank χ^(2),linear-trend χ^(2),likelihood-ratioχ2 statistics and Akaike information criterion(AIC)calculations,on which a modified pTNM classification with external validation using the SEER database was proposed.Results:Considerable stage migration,mainly for stage III,between the 8th and 7th editions was observed in both cohorts.The survival rates of subgroups of patients within stage IIIA,IIIB,or IIIC classified according to both editions were significantly different,demonstrating poor homogeneity for patient stratification.A modified pTNM staging system using data from the Chinese cohort was then formulated and demonstrated an improved homogeneity in these abovementioned subgroups.This staging system was further validated using data from the SEER cohort,and similar promising results were obtained.Compared with the 8th and 7th editions,the modified pTNM staging system displayed the highest log-rank χ^(2),linear-trend χ^(2),likelihood-ratio χ^(2),and lowest AIC values,indicating its superior discriminatory ability,monotonicity,homogeneity and prognosis prediction ability in both populations.Conclusions:The 8th edition of AJCC/UICC pTNM staging system is superior to the 7th edition,but still results in homogeneity in prognosis prediction.Our modified pTNM staging system demonstrated the optimal stratification and prognosis prediction ability in two large cohorts of different gastric cancer populations.

Bertalanffy-Pütter models for the first wave of the COVID-19 outbreak

The COVID-19 pandemics challenges governments across the world.To develop adequate responses,they need accurate models for the spread of the disease.Using least squares,we fitted Bertalanffy-Pütter(BP)trend curves to data about the first wave of the COVID-19 pandemic of 2020 from 49 countries and provinces where the peak of the first wave had been passed.BP-models achieved excellent fits(R-squared above 99%)to all data.Using them to smoothen the data,in the median one could forecast that the final count(asymptotic limit)of infections and fatalities would be 2.48 times(95%confidence limits 2.42-2.6)and 2.67 times(2.39-2.765)the total count at the respective peak(inflection point).By comparison,using logistic growth would evaluate this ratio as 2.00 for all data.The case fatality rate,defined as the quotient of the asymptotic limits of fatalities and confirmed infections,was in the median 4.85%(confidence limits 4.4%e6.5%).Our result supports the strategies of governments that kept the epidemic peak low,as then in the median fewer infections and fewer fatalities could be expected.