38602

Автор(ов): 

1

Параметры публикации
Тип публикации: 
Тезисы доклада
Название: 
Clustering of extremes in large-scale networks and its nonparametric analysis
Наименование конференции: 
3rd Conference of the International Society for Nonparametric Statistics (ISNPS-2016, Avignon, France)
Наименование источника: 
Book of abstracts of the 3rd Conference of the International Society for Nonparametric Statistics (ISNPS)
Город: 
Авиньон
Издательство: 
ISNPS
Год издания: 
2016
Страницы: 
57-58 http://www.isnpstat.org/images/ISNPS3/ISNPS_2016-Book_of_Abstracts.pdf
Аннотация
Clusters of consecutive exceedances of stochastic processes over sufficiently high threshold or conglomerates of extremes play an important role in the operating of complex large-scale systems in numerous applications. In \cite{Markovich1} and \cite{Markovich2} asymptotic geometric-like distributions of cluster and inter-cluster sizes are derived, where the cluster is determined as a number of consecutive exceedances over threshold between two consecutive non-exceedances. Considering distribution of an underlying process, its quantiles of sufficiently high levels serve as thresholds and their levels as probabilities in the geometric-like models of cluster and inter-cluster sizes. Expectations of the (inter-)cluster sizes are derived for the same conditions, too. Theoretically, these asymptotic models are obtained for sufficiently large sample sizes, (inter-)cluster sizes and thresholds. Since the models are invariant regarding the distribution of the process under study, one can apply it to stochastic sequences with unknown distributions. Based on these results, we obtain asymptotically equivalent distributions of other functions like cluster duration, return interval and first hitting time that depend on the cluster structure of the underlying process. We discuss applications of clusters of rare events to social networks and to the caching of the most popular documents transmitted through Internet in the short memory (cache) proposed in \cite{Markovich3}.
Библиографическая ссылка: 
Маркович Н.М. Clustering of extremes in large-scale networks and its nonparametric analysis / Book of abstracts of the 3rd Conference of the International Society for Nonparametric Statistics (ISNPS). Авиньон: ISNPS, 2016. С. 57-58 http://www.isnpstat.org/images/ISNPS3/ISNPS_2016-Book_of_Abstracts.pdf.