The fire frequency analysis branch of the pyrostatistics tree: sampling decisions and censoring in fire interval data

Statistical characterization of past fire regimes is important for both the ecology and management of fire-prone ecosystems. Survival analysis—or fire frequency analysis as it is often called in the fire literature—has increasingly been used over the last few decades to examine fire interval distributions. These distributions can be generated from a variety of sources (e.g., tree rings and stand age patterns), and analysis typically involves fitting the Weibull model. Given the widespread use of fire frequency analysis and the increasing availability of mapped fire history data, our goal has been to review and to examine some of the issues faced in applying these methods in a spatially explicit context. In particular, through a case study on the massive Cedar Fire in 2003 in southern California, we examine sensitivities of parameter estimates to the spatial resolution of sampling, point- and area-based methods for assigning sample values, current age surfaces versus historical intervals in generating distributions, and the inclusion of censored (i.e., incomplete) observations. Weibull parameter estimates were found to be roughly consistent with previous fire frequency analyses for shrublands (i.e., median age at burning of ~30–50 years and relatively low age dependency). Results indicate, however, that the inclusion or omission of censored observations can have a substantial effect on parameter estimates, far more than other decisions about specifics of sampling.

基于Weibull分布的煤体强度计算研究

以往矿山压力计算中多数使用煤体试件测试强度代替煤体强度进行计算,计算结果往往具有较大误差,针对此类问题,采用理论分析、实验室实验、数值模拟,数据拟合等手段研究了矿山工程中煤体强度的计算方法。结果表明:煤的强度具有一定的尺寸效应,测试试件边长越大,其强度越低;根据其尺寸特征,应用RFPA软件中的Weibull函数功能,模拟求解并拟合得出煤体强度与均质度和原煤强度之间的关系。定义了煤样标准强度为边长或直径为50 mm的煤试件强度,拟合得出煤样标准强度与原煤强度和煤体强度关系的表达式,可据此理论计算矿山工程中的煤体强度。     

A stochastic approach for the operation of a wind and pumped storage plant under a deregulated environment

To improve the competiveness in the energy market, it is necessary that the wind power plants provide guaranteed power generation, although, it is not possible to forecast power availability from wind power plant accurately. This paper presents a stochastic model and solution technique for the combined operation of wind and pumped storage power plants to improve the power availability and increasing the profit considering uncertainties of wind power generation. In this model, uncertainties in wind data have been forecasted for grid connected day-ahead market using Weibull distribution model. The imbalances in the forecasted wind data and the market demand have been reduced by operating the pumped storage power plant. In this stochastic mixed integer problem, pumped storage plant can take the supply either from the grid or from the wind power plant for the pumping operation to store the energy in order to utilize this energy during peak hours for increasing the overall revenue. The reliability of the pumped storage is improved by replacing the conventional unit with the adjustable speed type pumped storage unit. In order to prove the optimality of the solution, two case studies were considered. In case study–I, scheduling is provided by operating the conventional pumped storage unit, whereas in case study–II, adjustable speed pumped storage unit has been used. It has been found that the adjustable speed pumped storage unit has further reduced the imbalance between generated power and demand. The complete approach has been formulated and implemented using AMPL software.     

SOME SIMPLE MODELS FOR CONTINUOUS VARIATE TIME SERIES1

ABSTRACT: A survey is given of recently developed models for continuous variate non–Gaussian time series. The emphasis is on marginally specific models with given correlation structure. Exponential, Gamma, Weibull, Laplace, Beta and Mixed Exponential models are considered for the marginal distributions of the stationary time series. Most of the models are random coefficient, additive linear models. Some discussion of the meaning of autoregression and linearity is given, as well as suggestions for higher–order linear residual analysis for non–Gaussian models.     

A stratified model for the assessment of meteorologically adjusted trends of surface ozone

We consider the problem of assessing long-term trends of ozone concentrations measured on a single site located in an urban area. Among the many methods proposed in the literature to eliminate the confounding effect of changing weather conditions, we employ a stratification of daily maxima based on regression trees. Within each stratum conditional independence and Weilbull distribution are assumed for maxima. Long-term trend is defined non-parametrically by the sequence of yearly medians. Models are estimated following the Bayesian approach. The alternative assumptions of common and stratum specific trends are compared and a model with common trend for all strata is selected for the analyzed real dataset. The conditional independence assumption is checked by the comparison with a model including an autoregressive component.     

Qualitative and quantitative assessment of the risk from the exposure to fetotoxic chemical compounds

A new mathematical dose-response model for the expected probability of toxic response and also for the expected measure of the overdispersion parameter for the reproductive and developmental risk assessment is proposed. The model for the expected probability of toxic response is an improvised Weibull dose-response model incorporating the litter-size effect while the model for the overdispersion parameter is a polynomial function of the dose level. A beta-binomial distribution for the number of offspring showing toxic responses in a litter satisfactorily accounts for the extra-binomial variation and the intralitter correlation of responses of these pups. Confidence limits for low-dose extrapolation are based on the asymptotic distribution of the likelihood ratio. The safe dose for human exposure is then calculated by simple linear extrapolation. The model for overdispersion allows us to obtain the estimates of the overdispersion parameter at these dosages. This was not possible in the earlier models. The proposed model is illustrated by an application to a study on the effect of exposure to diethylhexylphthalate in mice. The results are compared with those obtained by Chen and Kodell (1989) who have applied the simple Weibull dose-response model to the same data set.This paper was prepared with partial support from the United States Environmental Protection Agency under a Cooperative Agreement Number CR-815273. The contents have not been subject to Agency review and therefore do not necessarily reflect the views or policies of the Agency and no official endorsement should be inferred.     

基于两参数Weibull模型的预腐蚀2A12铝合金材料裂纹萌生寿命评估

铝合金在航空工业中广泛应用,因此对于铝合金构件的寿命评估很重要。腐蚀损伤使得裂纹容易萌生,因此降低铝合金结构的疲劳寿命。铝合金构件在其服役过程中,裂纹萌生寿命占据了大部分的时间,研究腐蚀损伤对于铝合金材料的裂纹萌生寿命的影响具有重要意义。由于腐蚀疲劳影响因素众多,数据分散性很大,因此本文引入weibull分布模型评估腐蚀疲劳裂纹扩展,对于损伤容限评估具有重要意义。     

基于无线电探空资料反演大气水汽资源的垂直层结特征

利用1999-2009年的探空资料分析北京地区对流层大气水汽资源的垂直层结特征,采用韦伯和指数分布拟合大气水汽密度的概率密度函数。初步结果表明,各层拟合均通过卡方拟合优度检验,拟合相关系数高,精度高,均方根误差小;韦伯和指数拟合平均相关系数分别为0.93、0.95;拟合均方根误差分别为0.009、 0.01 g/m³,北京地区大气水汽资源的垂直分布符合指数分布规律;有降水时,对流层水汽密度有一定的垂直层状结构,无降水时,水汽密度随高度增加递减。     

基于存活概率的动态车龄分布模型

城市车辆的年龄组成(简称车龄分布)是体现城市车辆老化程度和确定车辆报废年限的重要指标。目前已有的车龄分布算法要求数据量大,在我国大部分城市很难得到完整的数据。笔者提出一种符合威布尔分布的车辆存活概率算法。该算法根据车辆保有量数据和报废车辆总数(或新车数据)推导出各年的车龄分布,且能够动态预测将来年份的车龄分布。同时,利用北京市小客数据对算法进行了实例应用,证明该法的实用可行性。由于该算法所需数据量小,计算简便,特别适用于我国在用车统计不完备的地区,利用该算法根据有限的数据来推导出当地的车龄分布,具有通用性。该算法的有效性检验和敏感度分析需进一步研究。     

STOCHASTIC FLOW DURATION CURVES FOR EVALUATION OF FLOW REGIMES IN RIVERS1

ABSTRACT: A stochastic estimation of low flow in the upper reaches of streams is needed for the planning, development, and management of water resources and/or water use systems. In this paper, the definition and development procedure for the stochastic flow duration curve is presented and applied to five catchments located in eastern Japan and to two catchments in western Thailand. The probability distribution of N‐year daily discharge data is extracted at various percentages of time for which specified discharges are equaled or exceeded in a water year. Such a distribution is usually represented with a straight line on log‐normal probability paper. However, some of the probability plots for the annual minimum daily discharge are best represented with a straight line on Weibull probability paper. The effectiveness of the stochastic flow duration curve defined for the evaluation of flow regime is illustrated through its application. The ten year probability for the discharge exceeded 97 percent of the time may be recognized as an index of low flow. The recession shape of the lower part of the flow duration curve is dependent on the strength of low flow persistence.