Starting from consideration that urban intersections are sites with promise for safety and operational improvements, the paper describes the steps taken to develop a crash predictive model for estimating the safety performance of urban unsignalized intersections located in Palermo, Italy. The focus is on unsignalized four-legged one-way intersections widespread in Italian downtowns. The sample considered in the study consist of 92 intersections in Palermo, Italy. For the study were collected crashes occurred in the sites during the years 2006-2012, geometric design and functional characteristics and traffic flow. Results showed that data were overdispersed and NB1 distributed. In order to account for the correlation within responses Generalized Estimating Equations (GEE) were used under different working correlation matrices.
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In the OSL dating of sediment, the scatter in equivalent dose (De) between grains is almost always larger than would be expected due to counting statistics alone. Some scatter may be caused by insufficient (partial) bleaching of some of the grains prior to deposition. In order to date partially bleached sediment, it is essential to estimate the amount of scatter caused by other processes (e.g. grain-to-grain variability in the natural dose rate). Measurements of such scatter are performed at the single-grain level; by contrast, most OSL dating is performed on multi-grain subsamples, for which grain-to-grain scatter is reduced through averaging. Here we provide a model for estimating the expected scatter (i.e. excluding that caused by partial bleaching) for multi-grain aliquots. The model requires as input the single-grain sensitivity distribution, the number of grains in the sub-samples, and the expected scatter at the single-grain level, all of which can be estimated to an adequate degree. The model compares well with measured values of scatter in De, determined using aliquots of various sizes, and can be used to help produce a minimum-age De from multi-grain subsamples that is consistent with single-grain data.
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The geometric distribution leads to a Lévy process parameterized by the probability of success. The resulting negative binomial process (NBP) is a purely jump and non-decreasing process with general negative binomial marginal distributions. We review various stochastic mechanisms leading to this process, and study its distributional structure. These results enable us to establish strong convergence of the NBP in the supremum norm to the gamma process, and lead to a straightforward algorithm for simulating sample paths. We also include a brief discussion of estimation of the NPB parameters, and present an example from hydrology illustrating possible applications of this model.
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