Statistical Methodology 

Abstract: A general family of univariate distributions generated by beta random variables, proposed by Jones, has been discussed recently in the literature. This family of distributions possesses great flexibility while fitting symmetric as well as skewed models with varying tail weights. In a similar vein, we define here a family of univariate distributions generated by Stacy’s generalized gamma variables. For these two families of univariate distributions, we discuss maximum entropy characterizations under suitable constraints. Based on these characterizations, an expected ratio of quantile densities is proposed for the discrimination of members of these two broad families of distributions. Several special cases of these results are then highlighted. An alternative to the usual method of moments is also proposed for the estimation of the parameters, and the form of these estimators is particularly amenable to these two families of distributions.

Abstract: A two-parameter family of distributions on (0,1) is explored which has many similarities to the beta distribution and a number of advantages in terms of tractability (it also, of course, has some disadvantages). Kumaraswamy’s distribution has its genesis in terms of uniform order statistics, and has particularly straightforward distribution and quantile functions which do not depend on special functions (and hence afford very easy random variate generation). The distribution might, therefore, have a particular role when a quantile-based approach to statistical modelling is taken, and its tractability has appeal for pedagogical uses. To date, the distribution has seen only limited use and development in the hydrological literature.

Abstract: There is a vast amount of literature regarding the asymptotic properties of various approaches to estimating simultaneous space–time panel models, but little attention has been paid to how the model estimates should be interpreted. The motivation for the use of space–time panel models is that they can provide us with information not available from cross-sectional spatial regressions. LeSage and Pace (2009) [7] showed that cross-sectional simultaneous spatial autoregressive models can be viewed as a limiting outcome of a dynamic space–time autoregressive process. A valuable aspect of dynamic space–time panel data models is that the own- and cross-partial derivatives that relate changes in the explanatory variables to those that arise in the dependent variables are explicit. This allows us to employ parameter estimates from these models to quantify dynamic responses over time and space as well as space–time diffusion impacts. We illustrate our approach using the demand for cigarettes over a 30 year period from 1963–1992, where the motivation for spatial dependence is a bootlegging effect where buyers of cigarettes near state borders purchase in neighboring states if there is a price advantage to doing so.

Abstract: We evaluate the performance of an extensive family of ARCH models in modelling daily Valueat-Risk (VaR) of perfectly diversified portfolios in five stock indices, using a number of distributional assumptions and sample sizes. We find, first, that leptokurtic distributions are able to produce better one-step-ahead VaR forecasts; second, the choice of sample size is important for the accuracy of the forecast, whereas the specification of the conditional mean is indifferent. Finally, the ARCH structure producing the most accurate forecasts is different for every portfolio and specific to each equity index.

Abstract: Sequential multi-chart detection procedures for detecting changes in multichannel sensor systems are developed. In the case of complete information on pre-change and post-change distributions, the detection algorithm represents a likelihood ratio-based multichannel generalization of Page’s cumulative sum (CUSUM) test that is applied to general stochastic models that may include correlated and nonstationary observations. There are many potential application areas where it is necessary to consider multichannel generalizations and general statistical models. In this paper our main motivation for doing so is network security: rapid anomaly detection for an early detection of attacks in computer networks that lead to changes in network traffic. Moreover, this kind of application encourages the development of a nonparametric multichannel detection test that does not use exact pre-change (legitimate) and post-change (attack) traffic models. The proposed nonparametric method can be effectively applied to detect a wide variety of attacks such as denial-of-service attacks, worm-based attacks, port-scanning, and man-in-the-middle attacks. In addition, we propose a multichannel CUSUM procedure that is based on binary quantized data; this procedure turns out to be more efficient than the previous two algorithms in certain scenarios. All proposed detection algorithms are based on the change-point detection theory. They utilize the thresholding of test statistics to achieve a fixed rate of false alarms, while allowing changes in statistical models to be detected “as soon as possible”. Theoretical frameworks for the performance analysis of detection procedures, as well as results of Monte Carlo simulations for a Poisson example and results of detecting real flooding attacks, are presented.