Specifying a joint space- and time-lag using a bivariate Poisson distribution

Separate space- or time-lags have been considered regularly in data analyses; as space–time models are more recently being studied extensively in data analytic fashion, joint estimation of both lags has to be considered explicitly. This paper addresses this issue, taking into special consideration parametric parsimony together with specification richness; use of the bivariate Poisson frequency distribution is advocated and applied to an empirical case. The relation of this approach to random effects specifications is investigated. Data for Belgian regional products constitute the empirical case study.

Seasonality and duration in extreme value distributions of significant wave height

This paper presents a statistical model to characterize the long-term extreme value distribution of significant wave height, conditioning to the duration of the storm and accounting for seasonality. A time-dependent version of the peak over threshold (POT) approach is used to build the model, which is then applied to specific reanalysis time series and NOAA buoy records. The model considers the annual and semiannual cycles which are parameterized in terms of harmonic functions. The inclusion of seasonal variabilities substantially reduces the residuals of the fitted model. The information obtained in this study can be useful to design maritime works, because (a) the model improves the understanding of the variability of extreme wave climate along a year and (b) the model accounts for the duration of the storm, which is a key parameter in several formulations for rubble mound breakwater design.     

Statistical analysis and long-term prediction of seismicity for linear zones

The model of the Poisson point process is too vague for earthquake locations in space and time: earthquakes tend to cluster in middle distances and to repulse in large ones. The Poisson point model with variable density makes it possible to describe the tendency for clustering but does not reveal the periodicity of clusters. The author proposes the point-process model where locations of points are determined not by densities of point distribution, but by densities of interpoint differences distribution. In the model, a latent periodicity is revealed and used for prediction of a point process. In 1983, the point-process model prediction was made for the Kuril Islands for 1983–1987 and two signs of danger in time and location were determined. Then they were confirmed by strong earth-quakes. In 1989, a similar prediction was made for North Armenia. The Spitak earthquake in 1988 is clearly seen from the data of previous earthquakes.     

The first and the second e of the extreme value distribution,EV1

In the peak over threshold model resulting in the Extreme-value distribution, type I, (EV1) the firste of the distribution function is based on the Poisson number of exceedances, and the seconde arises from the Exponentially distributed magnitudes.This paper, on the one hand, generalises the Poisson model to the (positive and negative) Binomial distribution, and, on the other hand, the Exponential distribution is generalised to the Generalised Pareto distribution. Lack of fit with respect to the Poisson and Exponential distribution is measured by statistics derived from those which would be locally most powerful if the estimates of the location and scale parameter were equal to the true parameter values. Ways of combining both statistics are discussed.     

Hypotheses for earthquake occurrences

Very little work has been done in generating alternatives to the Poisson process model. The work reported here deals with alternatives to the Poisson process model for the earthquakes and checks them using empirical data and the statistical hypothesis testing apparatus. The strategy used here for generating hypotheses is to compound the Poisson process. The parameter of the Poisson process is replaced by a random variable having prescribed density function. The density functions used are gamma, chi and extended (gamma/chi). The original distribution is then averaged out with respect to these density functions. For the compound Poisson processes the waiting time distributions for the future events are derived. As the parameters for the various statistical models for earthquake occurrences are not known, the problem is basically of composite hypothesis testing. One way of designing a test is to estimate these parameters and use them as true values. Momentmatching is used here to estimate the parameters. The results of hypothesis testing using data from Hindukush and North East India are presented.     

Risk assessment for the Yucca Mountain high-level nuclear waste repository site: Estimation of volcanic disruption

In this article, we model the volcanism near the proposed nuclear waste repository at Yucca Mountain, Nevada, U.S.A. by estimating the instantaneous recurrence rate using a nonhomogeneous Poisson process with Weibull intensity and by using a homogeneous Poisson process to predict future eruptions. We then quantify the probability that any single eruption is disruptive in terms of a (prior) probability distribution, since not every eruption would result in disruption of the repository. Bayesian analysis is performed to evaluate the volcanic risk. Based on the Quaternary data, a 90% confidence interval for the instantaneous recurrence rate near the Yucca Mountain site is (1.85×10^–6/yr, 1.26×10^–5/yr). Also, using-these confidence bounds, the corresponding 90% confidence interval for the risk (probability of at least one disruptive eruption) for an isolation time of 10⁴ years is (1.0×10^–3, 6.7×10^–3), if it is assumed that the intensity remains constant during the projected time frame.     

Completely Integrable Systems Connected with Lie Algebras

In a recent paper Ballersteros and Ragnisco (1998) have proposed a new method of constructing integrable Hamiltonian systems. A new class of integrable systems may be devised using the following sequence: , where A is a Lie algebra is a Lie–Poisson structure on R ₃, C is a Casimir for is a reduced Poisson bracket and (A, ▵) is a bialgebra. We study the relation between a Lie-Poisson stucture Λ and a reduced Poisson bracket , which is a key element in using the Lie algebra A to constructing this sequence. New examples of Lie algebras and their related integrable Hamiltonian systems are given. This revised version was published online in July 2006 with corrections to the Cover Date.     

基于非等间距泊松曲线在沉降预测中的应用

泊松曲线是一种精度较高的沉降预测方法，但是它只能在等时距数据条件下方能使用，在工程实际中很难满足这一要求。本文采用插值法将非等时距数据转化成等时距数列，并结合高层建筑沉降监测工程实例分析，结果表明，用泊松曲线模型预测建筑物沉降量与实际沉降量比较接近，具有较高的应用价值。