We discuss the analysis of the extremes of data by modelling the sizes and occurrence of exceedances over high thresholds. The natural distribution for such exceedances, the generalized Pareto distribution, is described and its properties elucidated. Estimation and model-checking procedures for univariate and regression data are developed, and the influence of and information contained in the most extreme observations in a sample are studied. Models for seasonality and serial dependence in the point process of exceedances are described. Sets of data on river flows and wave heights are discussed, and an application to the siting of nuclear installations is described.

Trade credit is created whenever a supplier offers terms that allow the buyer to delay payment. In this paper we document the rich variation in interfirm credit terms and credit policies across industries. We examine empirically the firm's basic credit policy choices: whether to extend credit or to require cash payment; and, if credit is extended, whether to adopt simple net terms or terms with discounts for prompt payment. We also examine determinants of variations in two-part terms. Results are supportive primarily of theories that explain credit terms as contractual solutions to information problems concerning product quality and buyer creditworthiness.TRADE CREDIT HAS IMPORTANT ECONOMIC SIGNIF ICANCE from both micro-and macroeconomic perspectives. During the 1990s vendor financing has accounted for an average $1.5 trillion of the book value of all assets of U.S. corporations and has represented approximately 2.5 times the combined value of all new public debt and primary equity issues during a given year. As a component of the money supply, trade credit, in the form of accounts payable, exceeds the primary money supply~M1! by a factor of 1.5 on average. 1 Clearly, efforts to control economic growth through monetary policy can be confounded by aggregate decisions of businesses to increase or decrease reliance on trade-credit financing.Several recent empirical studies examine determinants of firm reliance on trade credit. 2 These studies model supply and demand for trade credit using financial-statement data~accounts receivable and payable!. 3 However, many aspects of trade-credit practice are unexplored. Most notably, little is known about the types of credit terms~e.g., net 30, 2010 net 30! and credit policies that are observed across firms and industries.

A Bayesian statistical model is proposed that combines information from a multi-model ensemble of atmosphere-ocean general circulation models and observations to determine probability distributions of future temperature change on a regional scale. The posterior distributions derived from the statistical assumptions incorporate the criteria of bias and convergence in the relative weights implicitly assigned to the ensemble members. This approach can be considered an extension and elaboration of the Reliability Ensemble Averaging method. For illustration, we consider output of mean surface temperature from 9 AOGCMs, run under the A2 SRES scenario, for Boreal winter and summer, aggregated over 22 land regions. The shapes of the final probability density functions of temperature change vary widely, from unimodal curves for regions where model results agree, or outlying projections are discounted due to bias, to multimodal curves where models that cannot be discounted on the basis of bias give diverging projections. Besides the basic statistical model, we consider including correlation between present and future temperature responses, and test alternative forms of probability distributions for the model error terms. We suggest that a probabilistic approach, particularly in the form of a Bayesian model, is a useful platform from which to synthesize the information from an ensemble of simulations, at regional scales. The probability distributions of temperature change reveal features such as multi-modality and long tails that could not otherwise be easily discerned. Furthermore, the Bayesian model can serve as an interdisciplinary tool through which climate modelers, climatologists, and statisticians can work more closely. For example, climate modelers, through their expert judgment, could contribute to the formulations of prior distributions in the statistical model.

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Maximum likelihood and Bayesian estimators are developed and compared for the three-parameter Weibull distribution. For the data analysed in the paper, the two sets of estimators are found to be very different. The reasons for this are explored, and ways of reducing the discrepancy, including reparametrization, are investigated. Our overall conclusion is that there are practical advantages to the Bayesian approach.