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MA348exam 1998

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MA348exam 1998 pdf

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MA167exam01

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Local and average structure in zinc cyanide: towards an understanding of the atomistic origin of negative thermal expansion

Neutron diffraction at 11.4 and 295 K and solid-state 67Zn NMR are used to determine both the local and average structures in the disordered, negative thermal expansion (NTE) material, Zn(CN)2. Solid-state NMR not only confirms that there is head-to-tail disorder of the C≡N groups present in the solid, but yields information about the relative abundances of the different Zn(CN)4-n(NC)n tetrahedral species, which do not follow a simple binomial distribution. The Zn(CN)4 and Zn(NC)4 species occur with much lower probabilities than are predicted by binomial theory, supporting the conclusion that they are of higher energy than the other local arrangements. The lowest energy arrangement is Zn(CN)2(NC)2. The use of total neutron diffraction at 11.4 K, with analysis of both the Bragg diffraction and the derived total correlation function, yields the first experimental determination of the individual Zn−N and Zn−C bond lengths as 1.969(2) and 2.030(2) Å, respectively. The very small difference in bond lengths, of ~0.06 Å, means that it is impossible to obtain these bond lengths using Bragg diffraction in isolation. Total neutron diffraction also provides information on both the average and local atomic displacements responsible for NTE in Zn(CN)2. The principal motions giving rise to NTE are shown to be those in which the carbon and nitrogen atoms within individual Zn−C≡N−Zn linkages are displaced to the same side of the Zn···Zn axis. Displacements of the carbon and nitrogen atoms to opposite sides of the Zn···Zn axis, suggested previously in X-ray studies as being responsible for NTE behavior, in fact make negligible contribution at temperatures up to 295 K.

On the clustering of winter storm loss events over Germany

During the last decades, several windstorm series hit Europe leading to large aggregated losses. Such storm series are examples of serial clustering of extreme cyclones, presenting a considerable risk for the insurance industry. Clustering of events and return periods of storm series for Germany are quantified based on potential losses using empirical models. Two reanalysis data sets and observations from German weather stations are considered for 30 winters. Histograms of events exceeding selected return levels (1-, 2- and 5-year) are derived. Return periods of historical storm series are estimated based on the Poisson and the negative binomial distributions. Over 4000 years of general circulation model (GCM) simulations forced with current climate conditions are analysed to provide a better assessment of historical return periods. Estimations differ between distributions, for example 40 to 65 years for the 1990 series. For such less frequent series, estimates obtained with the Poisson distribution clearly deviate from empirical data. The negative binomial distribution provides better estimates, even though a sensitivity to return level and data set is identified. The consideration of GCM data permits a strong reduction of uncertainties. The present results support the importance of considering explicitly clustering of losses for an adequate risk assessment for economical applications.

A flexible model for survival data with a cure rate: a Bayesian approach

In this paper we deal with a Bayesian analysis for right-censored survival data suitable for populations with a cure rate. We consider a cure rate model based on the negative binomial distribution, encompassing as a special case the promotion time cure model. Bayesian analysis is based on Markov chain Monte Carlo (MCMC) methods. We also present some discussion on model selection and an illustration with a real dataset.

A hands-on approach for fitting long-term survival models under the GAMLSS framework

In many data sets from clinical studies there are patients insusceptible to the occurrence of the event of interest. Survival models which ignore this fact are generally inadequate. The main goal of this paper is to describe an application of the generalized additive models for location, scale, and shape (GAMLSS) framework to the fitting of long-term survival models. in this work the number of competing causes of the event of interest follows the negative binomial distribution. In this way, some well known models found in the literature are characterized as particular cases of our proposal. The model is conveniently parameterized in terms of the cured fraction, which is then linked to covariates. We explore the use of the gamlss package in R as a powerful tool for inference in long-term survival models. The procedure is illustrated with a numerical example. (C) 2009 Elsevier Ireland Ltd. All rights reserved.