# 29377

Автор(ов):

1

Параметры публикации
Тип публикации:
Пленарный доклад
Название:
Inferences for clusters of extreme values: modeling, distributions, applications
Электронная публикация:
Да
Наименование конференции:
Conference on Extreme Value Theory and Laws of Rare Events (Марсель, 2014)
Наименование источника:
Proceedings of the Conference on Extreme Value Theory and Laws of Rare Events (Марсель, 2014)
Город:
Марсель
Издательство:
CIRM
Год издания:
2014
Страницы:
http://www.mcs.st-and.ac.uk/~miket/CIRM_extremes14/CIRM_extreme.html
Аннотация
Extremes in stochastic sequences arising as clusters of exceedances over a threshold are observed in numerous applications of climate research, finance, telecommunication and social systems. Such clusters are caused by dependence. We define the cluster as a conglomerate containing consecutive exceedances of the underlying process $\{R_n\}$ over a threshold $u$ separated by return intervals with consecutive non-exceedances. The geometric-like limit distributions of the cluster size %$T_2(x_{\rho_n})$ and inter-cluster size are obtained in Markovich-2014 under the mixing condition similar to one used in \cite{Ferro}. The sequence of high $(1-\rho_n)$-order quantiles $x_{\rho_n}$ of the $\{R_n\}$ is used as thresholds. The obtained distributions differ from the geometric distribution by the extremal index of the process $\{R_n\}$. The asymptotic first moments of both cluster characteristics are obtained \cite{Markovich-2013}, \cite{Markovich-2014}. Similarly, the result can be extended to moments of higher orders. In \cite{Markovich-2014} the duration of (inter-)clusters is defined as a sum of the random number of weakly dependent, regularly varying inter-arrival times between events of interest with tail index \$0
Библиографическая ссылка:
Маркович Н.М. Inferences for clusters of extreme values: modeling, distributions, applications / Proceedings of the Conference on Extreme Value Theory and Laws of Rare Events (Марсель, 2014). Марсель: CIRM, 2014. С. http://www.mcs.st-and.ac.uk/~miket/CIRM_extremes14/CIRM_extreme.html.