Gumbel分布统计参数估计方法及其应用

依据Gumbel分布理论,给出了Gumbel频率分析的统计参数估计方法(含连续系列和不连续系列)。以往的Gumbel频率分析主要用于涉水工程的设计水位(潮位)及设计暴雨洪水分析;随着国民经济的快速发展,在我国大型基建工程对于气温、风速等极端气象要素的规划与设计中,普遍采用Gumbel分布进行相关要素的设计分析计算。实例研究表明,当极值系列中出现历史特大值时,应考虑特大值的重现期,并需结合当地的区域水文气象特性等进行合理性分析。

线性矩法的特点评析和应用问题

介绍了线性矩法的无偏估计与直接计算的关系,讨论了在概率权重矩计算过程中各系列之间的高度相关性及其对结果的影响,建立了直接计算线性矩法的Cv和Cs近似公式,叙述了适线问题和相应的经验频率公式。文中认为,水文频率计算时,由于资料的随机性和处理方法上的概化性,故用任何计算方法得到的结果,具有不同程度的不确定性,只能作为估计的初值,需通过时空上综合平衡,再经合理性分析和调整后,才能取用。

水文频率计算中对数Γ分布的应用

简述了对数Γ分布的统计特性和不同CS／CV值时模比系数Kp的制作方法。介绍了估计参数的矩法、混合矩法和适线法。文中认为，可以用水文资料的原系列直接进行频率计算，以避免对数变换引起的误差；并且，可将该型分布作为比较线型，用于进一步的分析研究中。

连续系统可靠性分析方法研究

由于对管道、钢缆这样的典型连续系统进行可靠性评价比较困难,因此不能将管道作为一个元件对待,须将连续系统看成由若干单元组成的一个"串联系统"。首先,应用最小次序统计量推导出连续系统强度分布函数的Weibull表达式,并通过参数变换确定连续系统的强度分布。而且强度分布能通过实验所确定的参数来表示。然后,应用最大似然估计法对连续系统强度分布的参数进行估计,并应用系统级的应力-强度干涉模型计算连续系统的可靠度。最后讨论连续系统可靠度的极值问题,为管道、钢缆类连续系统的可靠性评价提供依据。

Statistical Analysis for the Birnbaum-Saunders Fatigue Life Distribution under Type-Ⅱ Bilateral Censoring and Multiply Type-II Censoring

In present paper, we obtain the inverse moment estimations of parameters of the Birnbaum-Saunders fatigue life distribution based on Type-Ⅱ bilateral censored samples and multiply Type-Ⅱ censored sample. In this paper, we also get the interval estimations of the scale parameters.

Modelling of Wage and Income Distributions Using the Method of L-Moments

Commonly used statistical procedure to describe the observed statistical sets is to use their conventional moments or cumulants. When choosing an appropriate parametric distribution for the data set is typically that parameters of a parametric distribution are estimated using the moment method of creating a system of equations in which the sample conventional moments lay in the equality of the corresponding moments of the theoretical distribution. However, the moment method of parameter estimation is not always convenient, especially for small samples. An alternative approach is based on the use of other characteristics, which the author calls L-moments. L-moments are analogous to conventional moments, but they are based on linear combinations of order statistics, i.e., L-statistics. Using L-moments is theoretically preferable to the conventional moments and consists in the fact that L-moments characterize a wider range of distribution. When estimating from sample L-moments, L-moments are more robust to the presence of outliers in the data. Experience also shows that, compared to conventional moments, L-moments are less prone to bias of estimation. Parameter estimates obtained using L-moments are mainly in the case of small samples often even more accurate than estimates of parameters made by maximum likelihood method. Using the method of L-moments in the case of small data sets from the meteorology is primarily known in statistical literature. This paper deals with the use of L-moments in the case for large data sets of income distribution （individual data） and wage distribution （data are ordered to form of interval frequency distribution of extreme open intervals）. This paper also presents a comparison of the accuracy of the method of L-moments with an accuracy of other methods of point estimation of parameters of parametric probability distribution in the case of large data sets of individual data and data ordered to form of interval frequency distribution.

Design of motion control of dam safety inspection underwater vehicle

Plenty of dams in China are in danger while there are few effective methods for underwater dam inspections of hidden problems such as conduits,cracks and inanitions.The dam safety inspection remotely operated vehicle(DSIROV) is designed to solve these problems which can be equipped with many advanced sensors such as acoustical,optical and electrical sensors for underwater dam inspection.A least-square parameter estimation method is utilized to estimate the hydrodynamic coefficients of DSIROV,and a four degree-of-freedom(DOF) simulation system is constructed.The architecture of DSIROV's motion control system is introduced,which includes hardware and software structures.The hardware based on PC104 BUS,uses AMD ELAN520 as the controller's embedded CPU and all control modules work in VxWorks real-time operating system.Information flow of the motion system of DSIROV,automatic control of dam scanning and dead-reckoning algorithm for navigation are also discussed.The reliability of DSIROV's control system can be verified and the control system can fulfill the motion control mission because embankment checking can be demonstrated by the lake trials.

Unbiased parameter estimation of continuous-time system based on modulating functions with input and output white noises

An efficient unbiased estimation method is proposed for the direct identification of linear continuous-time system with noisy input and output measurements.Using the Gaussian modulating filters,by numerical integration,an equivalent discrete identification model which is parameterized with continuous-time model parameters is developed,and the parameters can be estimated by the least-squares (LS) algorithm.Even with white noises in input and output measurement data,the LS estimate is biased,and the bias is determined by the variances of noises.According to the asymptotic analysis,the relationship between bias and noise variances is derived.One equation relating to the measurement noise variances is derived through the analysis of the LS errors.Increasing the degree of denominator of the system transfer function by one,an extended model is constructed.By comparing the true value and LS estimates of the parameters between original and extended model,another equation with input and output noise variances is formulated.So,the noise variances are resolved by the set of equations,the LS bias is eliminated and the unbiased estimates of system parameters are obtained.A simulation example by comparing the standard LS with bias eliminating LS algorithm indicates that the proposed algorithm is an efficient method with noisy input and output measurements.

对数Γ分布在水文计算中的应用

简述了对数Γ分布的统计特性和不同Ｃｓ／Ｃｙ比值时模比系数的制作方法，。介绍了水文系列估计参数的矩法和三点适线法。文中认为可以将该型曲线作为比较线型，用于常用分布配适不佳时，或用于进一步的分析、比较和研究中。

Corrected empirical likelihood for a class of generalized linear measurement error models

Generalized linear measurement error models, such as Gaussian regression, Poisson regression and logistic regression, are considered. To eliminate the effects of measurement error on parameter estimation, a corrected empirical likelihood method is proposed to make statistical inference for a class of generalized linear measurement error models based on the moment identities of the corrected score function. The asymptotic distribution of the empirical log-likelihood ratio for the regression parameter is proved to be a Chi-squared distribution under some regularity conditions. The corresponding maximum empirical likelihood estimator of the regression parameter π is derived, and the asymptotic normality is shown. Furthermore, we consider the construction of the confidence intervals for one component of the regression parameter by using the partial profile empirical likelihood. Simulation studies are conducted to assess the finite sample performance. A real data set from the ACTG 175 study is used for illustrating the proposed method.

Using the BirdTree.org website to obtain robust phylogenies for avian comparative studies： A primer

Comparative studies of trait evolution require accounting for the shared evolutionary history. This is done by includ- ing phylogenetic hypotheses into statistical analyses of species＇ traits, for which birds often serve as excellent models. The online publication of the most complete molecular phylogeny of extant bird species （www.birdtree.org, BirdTree hereafter） now allows evolutionary biologists to rapidly obtain sets of equally plausible phylogenetic trees for any set of species to be incorporated as a phylogenetic hypothesis in comparative analyses. We discuss methods to use BirdTree tree sets for comparative studies, either by building a consensus tree that can be incorporated into standard comparative analyses, or by using tree sets to account for the ef- fect of phylogenetie uncertainty. Methods accounting for phylogenetic uncertainty should be preferred whenever possible because they should provide more reliable parameter estimates and realistic confidence intervals around them. Based on a real compara- tive dataset, we ran simulations to investigate the effect of variation in the size of the random tree sets downloaded from BirdTree on the variability of parameter estimates from a bivariate relationship between mass-specific productivity and body mass. Irre- spective of the method of analysis, using at least 1,000 trees allows obtaining parameter estimates with very small （〈 0.15%） co- efficients of variation. We argue that BirdTree, due to the ease of use and the major advantages over previous ＇traditional＇ meth- ods to obtain phylogenetic hypotheses of bird species （e.g. supertrees or manual coding of published phylogenies）, will become the standard reference in avian comparative studies for years to come.

A linear varying coefficient ARCH-M model with a latent variable

Motivated by the psychological factor of time-varying risk-return relationship, this paper studies a linear varying coefficient ARCH-M model with a latent variable. Due to the unobservable property of the latent variable, a corrected likelihood method is employed for parametric estimation. Estimators are proved to be consistent and asymptotically normal under certain regularity conditions. A simple test statistic is also proposed for testing latent variable effect. Simulation results confirm that the proposed estimators and test perform well.The model is further applied to examine whether the risk-return relationship depends on investor's sentiment in American Market and some explainable results are obtained.