Richard L. Smith

SUMMARY We consider maximum likelihood estimation of the parameters of a probability density which is zero for x 2, the information matrix is finite and the classical asymptotic properties continue to hold. For cx = 2 the maximum likelihood estimators are asymptotically efficient and normally distributed, but with a different rate of convergence. For 1 < a < 2, the maximum likelihood estimators exist in general, but are not asymptotically normal, while the question of asymptotic efficiency is st

Several methods of analyzing extreme values are now known, most based on the extreme value limit distributions or related families. This paper reviews these techniques and proposes some extensions based on the point-process view of high-level exceedances. These ideas are illustrated with a detailed analysis of ozone data collected in Houston, Texas. There is particular interest in whether they is any trend in the data. The analysis reveals no trend in the overall levels of the series, but a mark

We study the asymptotic properties of estimators of the tail of a distribution based on the excesses over a threshold. A key idea is the use of Pickands' generalised Pareto distribution and its fitting, in most cases, by the method of maximum likelihood. The results cover all three limiting types of extreme value theory. We propose a new estimator for an index of regular variation and show that it often performs better than Hill's estimator. We give new results for estimating the endpoint of a d

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.

An efficient process for the dehydration of fructose into 5-hydroxymethylfurfural (5-HMF) in ionic liquid 1-butyl-3-methyl imidazolium chloride ([BMIM][Cl]) by using a sulfonic ion-exchange resin as catalyst was developed. A fructose conversion of 98.6% with a 5-HMF yield of 83.3% was achieved in 10 min reaction time at 80 °C. When the reaction temperature was increased to 120 °C, a 5-HMF yield of 82.2% was obtained in only 1 min for essentially 100% fructose conversion. No large decrease in 5-H

SUMMARY The extremal index is an important parameter measuring the degree of clustering of extremes in a stationary process. If we consider the point process of exceedance times over a high threshold, then this can be shown to converge asymptotically to a clustered Poisson process. The extremal index, a parameter in the interval [0, 1], is the reciprocal of the mean cluster size. Apart from being of interest in its own right, it is a crucial parameter for determining the limiting distribution of

Projections of future climate change caused by increasing greenhouse gases depend critically on numerical climate models coupling the ocean and atmosphere (GCMs). However, different models differ substantially in their projections, which raises the question of how the different models can best be combined into a probability distribution of future climate change. For this analysis, we have collected both current and future projected mean temperatures produced by nine climate models for 22 regions

This article examines the extent to which takeovers mitigate the underinvestment problem of S. C. Myers and N. S. Majluf (1984) and the free-cash-flow problem of M. C. Jansen (1986). Using accounting data, bidders are classified as 'high free cash flow,' 'slack poor,' or 'other.' Bidder, target, and total returns are highest for acquisitions that combine slack-poor and free-cash-flow firms. The widely cited negative returns of bidders are concentrated among combinations where bidders and targets

A bivariate time series regression approach is used to model observed variations in hemispheric mean temperature over the period 1900-96. The regression equations include deterministic predictor variables and lagged values of the two predictands, and two different forms of this basic structure are employed. The deterministic predictors considered are simple linear trends, various climate model-generated time series based on different combinations of greenhouse gas, sulfate aerosol, and solar for