关于我国地震灾害损失分布函数的研究

文章以1978～2006年间我国发生的183起地震灾害事故为样本,选取地震损失额、每年发生地震次数为指标,建立我国地震灾害损失分布函数。针对地震损失额利用经验剩余函数值分析损失分布集中程度、初步估计损失分布函数,分组处理样本数据、拟合分布图像、参数估计、单个样本非参数检验,确定损失分布函数为对数正态分布;针对每年发生地震灾害次数初步估计分布函数,通过历史频率与理论概率比较判断拟合效果、确定分布函数为泊松分布。     

基于Bayes估计理论的洪水水位概率变点研究

利用Bayes估计理论,研究洪水水位概率变点问题,给出一个确定变点存在的判断方法,通过具体例子进行讨论.     

基于帕累托分布的洪水贝叶斯分析

文章基于帕累托分布,运用贝叶斯估计理论研究了汛期洪水水位的分布规律,给出了相关参数的计算公式,并通过具体例子进行了讨论。     

基于期望的重要抽样方法研究

传统的Monte Carlo方法仿真稀有事件需要较长的时间,而重要抽样技术可以有效地缩短仿真时间,提高仿真效率.文章提出一种新的重要抽样实现方法,用来估计仿真模型中的稀有事件的概率;利用期望寻找最优重要抽样分布函数,并与传统的Monte Carlo算法进行比较.仿真结果显示了该方法在估计稀有事件概率方面的有效性.     

PERT网络活动时间参数估计的改进

PERT网络计划技术及Monte Carlo Simulation(MCS)求解PERT网络计划方法在工程项目的进度计划与控制中虽已广泛应用,但仍存在着不足。本文基于PERT网络分布的假设,阐述了常规三时估计方法的不足,并提出了相应解决对策,并采用限定概率三时估计法及拟合方差最小模型,分别对常规三时估计方法及常规!分布函数参数确定方法进行了改进。实例证实,限定概率三时估计法能统一网络活动时间估计标准,提高估计精度;拟合方差最小模型能提高分布函数确定精度。     

洪水频率分布的尾指数估计

洪灾风险分析中的一项重要内容是关于洪水频率分布的准确描述。文章首先基于指数回归模型给出了矩估计的门限值和样本点分割的选取原理和方法,然后利用MC方法,对Burr(1,1,1)、Frechet(1)、学生-t4等几种常见的极值分布进行模拟以验证模型,最后运用洞庭湖湖区周边四个水文观测站所观察到的洪水流量数据进行了实证分析,得到了洪水分布的尾指数估计。     

产品无失效概率的贝叶斯估计

对给定的一组泊松样本,在与信息论中的熵函数有关的一种对称损失函数下,用参数估计方法研究了产品无失效概率的贝叶斯估计与区间估计。在给定先验分布下得到了这两种估计的精确形式,并讨论了贝叶斯估计的可容许性,模拟结果表明文章得到的这两种估计都具有较高的精度。     

基于模糊回归模型的洪水灾害分级评估方法研究

高效、准确评估自然灾害事件的级别,是应急管理中有效控制灾害和制定减灾防灾对策的重要保证。针对洪水灾害等级评估中存在的模糊不确定特征,提出基于模糊多元回归模型的洪水灾害分级评估方法。首先,提出一种基于可能性均值-标准差距离的模糊多元回归模型的参数估计方法;然后,将洪水灾害等级和影响因素看成是模糊因变量和自变量,通过求解模糊回归方法得到模糊回归影响系数,这样能够较好地解决分级过程中存在的模糊性问题;最后,以45个洪水灾害事件为例,实例结果表明,模糊回归模型应用于自然灾害事件分级是可行且有效的,能够较好地解决灾害事件等级评估中的模糊性。     

浅谈Excel在统计分析中的应用（下）

三、用Excel计算分布的概率 利用Excel中的函数工具,可以计算二项分布、超几何分布、泊松分布、正态分布等概率分布的概率。下面以二项分布概率的计算为例,来说明如何用Excel计算分布的概率。 利用Excel的BINOMDIST函数可以计算出二项分布的概率以及累积概率。该函数有四个参数:Number-s(实验成功的次     

具有随机缺失协变量的广义变系数模型

在协变量随机缺失时,文章利用加权拟似然方法给出了广义变系数模型中非参数函数系数的估计。由估计的渐近性质可知,当缺失概率未知时,本文提出的方法与缺失概率已知时的估计的渐近性质类似。通过模拟表明加权拟似然估计要比仅用完整个体的方法要好。     

Efficient Estimation of the PDF and the CDF of the Exponentiated Gumbel Distribution

The exponentiated Gumbel model has been shown to be useful in climate modeling including global warming problem, flood frequency analysis, offshore modeling, rainfall modeling, and wind speed modeling. Here, we consider estimation of the probability density function (PDF) and the cumulative distribution function (CDF) of the exponentiated Gumbel distribution. The following estimators are considered: uniformly minimum variance unbiased (UMVU) estimator, maximum likelihood (ML) estimator, percentile (PC) estimator, least-square (LS) estimator, and weighted least-square (WLS) estimator. Analytical expressions are derived for the bias and the mean squared error. Simulation studies and real data applications show that the ML estimator performs better than others.     

Spatial modeling of extreme rainfall in northeast Thailand

It is well recognized that the generalized extreme value (GEV) distribution is widely used for any extreme events. This notion is based on the study of discrete choice behavior; however, there is a limit for predicting the distribution at ungauged sites. Hence, there have been studies on spatial dependence within extreme events in continuous space using recorded observations. We model the annual maximum daily rainfall data consisting of 25 locations for the period from 1982 to 2013. The spatial GEV model that is established under observations is assumed to be mutually independent because there is no spatial dependency between the stations. Furthermore, we divide the region into two regions for a better model fit and identify the best model for each region. We show that the regional spatial GEV model reflects the spatial pattern well compared with the spatial GEV model over the entire region as the local GEV distribution. The advantage of spatial extreme modeling is that more robust return levels and some indices of extreme rainfall can be obtained for observed stations as well as for locations without observed data. Thus, the model helps to determine the effects and assessment of vulnerability due to heavy rainfall in northeast Thailand.     

A new absolute continuous bivariate generalized exponential distribution

The generalized exponential is the most commonly used distribution for analyzing lifetime data. This distribution has several desirable properties and it can be used quite effectively to analyse several skewed life time data. The main aim of this paper is to introduce absolutely continuous bivariate generalized exponential distribution using the method of Block and Basu (1974). In fact, the Block and Basu exponential distribution will be extended to the generalized exponential distribution. We call the new proposed model as the Block and Basu bivariate generalized exponential distribution, then, discuss its different properties. In this case the joint probability distribution function and the joint cumulative distribution function can be expressed in compact forms. The model has four unknown parameters and the maximum likelihood estimators cannot be obtained in explicit form. To compute the maximum likelihood estimators directly, one needs to solve a four dimensional optimization problem. The EM algorithm has been proposed to compute the maximum likelihood estimations of the unknown parameters. One data analysis is provided for illustrative purposes. Finally, we propose some generalizations of the proposed model and compare their models with each other.     

地质灾害损失分布拟合与风险度量

 地质灾害的频繁发生已引起了社会各界的高度关注。本文以湖南省娄底市地质灾害损失数据为样本,借助广义Pareto分布和对数正态分布对地质灾害损失分布进行刻画,建立了一个分段的地质灾害损失分布模型,然后讨论了地质灾害损失的纯保费和最大可能损失的估计问题,得到了一些有意义的结果。     

Designing and integrating composite networks for monitoring multivariate gaussian pollution fields

Networks of ambient monitoring stations are used to monitor environmental pollution fields such as those for acid rain and air pollution. Such stations provide regular measurements of pollutant concentrations. The networks are established for a variety of purposes at various times so often several stations measuring different subsets of pollutant concentrations can be found in compact geographical regions. The problem of statistically combining these disparate information sources into a single 'network' then arises. Capitalizing on the efficiencies so achieved can then lead to the secondary problem of extending this network. The subject of this paper is a set of 31 air pollution monitoring stations in southern Ontario. Each of these regularly measures a particular subset of ionic sulphate, sulphite, nitrite and ozone. However, this subset varies from station to station. For example only two stations measure all four. Some measure just one. We describe a Bayesian framework for integrating the measurements of these stations to yield a spatial predictive distribution for unmonitored sites and unmeasured concentrations at existing stations. Furthermore we show how this network can be extended by using an entropy maximization criterion. The methods assume that the multivariate response field being measured has a joint Gaussian distribution conditional on its mean and covariance function. A conjugate prior is used for these parameters, some of its hyperparameters being fitted empirically.     

A seasonal mixed-POT model to estimate high flood quantiles from different event types and seasons

Flood events can be caused by several different meteorological circumstances. For example, heavy rain events often lead to short flood events with high peaks, whereas snowmelt normally results in events of very long duration with a high volume. Both event types have to be considered in the design of flood protection systems. Unfortunately, all these different event types are often included in annual maximum series (AMS) leading to inhomogeneous samples. Moreover, certain event types are underrepresented in the AMS. This is especially unsatisfactory if the most extreme events result from such an event type. Therefore, monthly maximum data are used to enlarge the information spectrum on the different event types. Of course, not all events can be included in the flood statistics because not every monthly maximum can be declared as a flood. To take this into account, a mixture Peak-over-threshold model is applied, with thresholds specifying flood events of several types that occur in a season of the year. This model is then extended to cover the seasonal type of the data. The applicability is shown in a German case study, where the impact of the single event types in different parts of a year is evaluated.     

On the modified Burr IV model for hydrological events: development,properties, characterizations and applications

We introduce a new distribution for modeling extreme events about frequency analysis called modified Burr IV (MBIV) distribution. We derive the MBIV distribution on the basis of the generalized Pearson differential equation. The proposed model turns out to be flexible: its density function can be symmetrical, right-skewed, left-skewed, J and bimodal shaped. Its hazard rate has shapes such as bathtub and modified bathtub, increasing, decreasing, and increasing-decreasing-increasing. To show the importance of the MBIV distribution, we establish various mathematical properties such as random number generator, sub-models, moments related properties, inequality measures, reliability measures, uncertainty measures and characterizations. We utilize the maximum likelihood estimation technique to estimate the model parameters. We assess the behavior of the maximum likelihood estimators (MLEs) of the MBIV parameters via a simulation study. Five data sets related to frequency analysis are considered to elucidate the significance of the MBIV distribution. We show that the MBIV model is the best model to analyze data for hydrological events, motivating its high level of adaptability in the applied setting.KEYWORDS: Characterizations, elasticity function, moments, maximum likelihood estimator, reliability     

Exact and Approximate Distributions of the Maximum Likelihood Estimate in a Simple Factor Analysis Model

We study a factor analysis model with two normally distributed observations and one factor. In the case when the errors have equal variance, the maximum likelihood estimate of the factor loading is given in closed form. Exact and approximate distributions of the maximum likelihood estimate are considered. The exact distribution function is given in a complex form that involves the incomplete Beta function. Approximations to the distribution function are given for the cases of large sample sizes and small error variances. The accuracy of the approximations is discussed     

A new class of skew distributions with climate data analysis

In this paper, we develop a new general class of skew distributions with flexibility properties on the tails. Moreover, such class can provide heavy and light tails. Some of its mathematical properties are studied, including the quantile function, the moments, the moment generating function and the mean of deviations. New skew distributions are derived and used to construct new models capturing asymmetry inherent to data. The estimation of the class parameters is investigated by the method of maximum likelihood and the performance of the estimators is assessed by a simulation study. Applications of the proposed distribution are explored for two climate data sets. The first data set concerns the annual heat wave index and the second data set involves temperature and precipitation measures from the meteorological station located at Schiphol, Netherlands. Data fitting results show that our models perform better than the competitors.