Modelling road accident blackspots data with the discrete generalized Pareto distribution

Extreme value modelling of SARS-CoV-2 community transmission using discrete generalized Pareto distributions

Superspreading has been suggested to be a major driver of overall transmission in the case of SARS-CoV-2. It is, therefore, important to statistically investigate the tail features of superspreading events (SSEs) to better understand virus propagation and control. Our extreme value analysis of different sources of secondary case data indicates that case numbers of SSEs associated with SARS-CoV-2 may be fat-tailed, although substantially less so than predicted recently in the literature, but also less important relative to SSEs associated with SARS-CoV. The results caution against pooling data from both coronaviruses. This could provide policy- and decision-makers with a more reliable assessment of the tail exposure to SARS-CoV-2 contamination. Going further, we consider the broader problem of large community transmission. We study the tail behaviour of SARS-CoV-2 cluster cases documented both in official reports and in the media. Our results suggest that the observed cluster sizes have been fat-tailed in the vast majority of surveyed countries. We also give estimates and confidence intervals of the extreme potential risk for those countries. A key component of our methodology is up-to-date discrete generalized Pareto models which allow for maximum likelihood-based inference of data with a high degree of discreteness.

Gradient boosting with extreme-value theory for wildfire prediction

This paper details the approach of the team Kohrrelation in the 2021 Extreme Value Analysis data challenge, dealing with the prediction of wildfire counts and sizes over the contiguous US. Our approach uses ideas from extreme-value theory in a machine learning context with theoretically justified loss functions for gradient boosting. We devise a spatial cross-validation scheme and show that in our setting it provides a better proxy for test set performance than naive cross-validation. The predictions are benchmarked against boosting approaches with different loss functions, and perform competitively in terms of the score criterion, finally placing second in the competition ranking.

A Comparative Study on Traffic Modeling Techniques for Predicting and Simulating Traffic Behavior

The significant advancements in intelligent transportation systems (ITS) have contributed to the increased development in traffic modeling. These advancements include prediction and simulation models that are used to simulate and predict traffic behaviors on highway roads and urban networks. These models are capable of precise modeling of the current traffic status and accurate predictions of the future status based on varying traffic conditions. However, selecting the appropriate traffic model for a specific environmental setting is challenging and expensive due to the different requirements that need to be considered, such as accuracy, performance, and efficiency. In this research, we present a comprehensive literature review of the research related to traffic prediction and simulation models. We start by highlighting the challenges in the long-term and short-term prediction of traffic modeling. Then, we review the most common nonparametric prediction models. Lastly, we look into the existing literature on traffic simulation tools and traffic simulation algorithms. We summarize the available traffic models, define the required parameters, and discuss the limitations of each model. We hope that this survey serves as a useful resource for traffic management engineers, researchers, and practitioners in this domain.

Assessing the Performance of the Discrete Generalised Pareto Distribution in Modelling Non-Life Insurance Claims

The generalised Pareto distribution (GPD) offers a family of probability spaces which support threshold exceedances and is thus suitable for modelling high-end actuarial risks. Nonetheless, its distributional continuity presents a critical limitation in characterising data of discrete forms. Discretising the GPD, therefore, yields a derived distribution which accommodates the count data while maintaining the essential tail modelling properties of the GPD. In this paper, we model non-life insurance claims under the three-parameter discrete generalised Pareto (DGP) distribution. Data for the study on reported and settled claims, spanning the period 2012–2016, were obtained from the National Insurance Commission, Ghana. The maximum likelihood estimation (MLE) principle was adopted in fitting the DGP to yearly and aggregated data. The estimation involved two steps. First, we propose a modification to the $\mu$ and $\left(\mu +1\right)$ frequency method in the literature. The proposal provides an alternative routine for generating initial estimators for MLE, in cases of varied count intervals, as is a characteristic of the claim data under study. Second, a bootstrap algorithm is implemented to obtain standard errors of estimators of the DGP parameters. The performance of the DGP is compared to the negative binomial distribution in modelling the claim data using the Akaike and Bayesian information criteria. The results show that the DGP is appropriate for modelling the count of non-life insurance claims and provides a better fit to the regulatory claim data considered.

A Mixture Model of Truncated Zeta Distributions with Applications to Scientific Collaboration Networks

The degree distribution has attracted considerable attention from network scientists in the last few decades to have knowledge of the topological structure of networks. It is widely acknowledged that many real networks have power-law degree distributions. However, the deviation from such a behavior often appears when the range of degrees is small. Even worse, the conventional employment of the continuous power-law distribution usually causes an inaccurate inference as the degree should be discrete-valued. To remedy these obstacles, we propose a finite mixture model of truncated zeta distributions for a broad range of degrees that disobeys a power-law behavior in the range of small degrees while maintaining the scale-free behavior. The maximum likelihood algorithm alongside the model selection method is presented to estimate model parameters and the number of mixture components. The validity of the suggested algorithm is evidenced by Monte Carlo simulations. We apply our method to five disciplines of scientific collaboration networks with remarkable interpretations. The proposed model outperforms the other alternatives in terms of the goodness-of-fit.

[Spatial analysis of road traffic accidents with fatalities in Spain, 2008-2011]

OBJECTIVE

To estimate the areas of greatest density of road traffic accidents with fatalities at 24 hours per km(2)/year in Spain from 2008 to 2011, using a geographic information system.

METHODS

Accidents were geocodified using the road and kilometer points where they occurred. The average nearest neighbor was calculated to detect possible clusters and to obtain the bandwidth for kernel density estimation.

RESULTS

A total of 4775 accidents were analyzed, of which 73.3% occurred on conventional roads. The estimated average distance between accidents was 1,242 meters, and the average expected distance was 10,738 meters. The nearest neighbor index was 0.11, indicating that there were aggregations of accidents in space. A map showing the kernel density was obtained with a resolution of 1 km(2), which identified the areas of highest density.

CONCLUSIONS

This methodology allowed a better approximation to locating accident risks by taking into account kilometer points. The map shows areas where there was a greater density of accidents. This could be an advantage in decision-making by the relevant authorities.