On the exceedance point process for a stationary sequence

Hsing, Tailen; Hüsler, Jürg; Leadbetter, M. R.

doi:10.1007/bf00718038

Cited by 228 publications

(129 citation statements)

References 16 publications

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“…These estimates can be further justified by the asymptotic statistical theory of Hsing et al [1988].…”

Section: The Distribution and The Clustering Of Fast Cmesmentioning

confidence: 90%

“…It is known from theory [Hsing et al, 1988] that if one focuses on asymptotically larger and larger thresholds U, the time intervals t i between the fast CMEs will converge (under time-rescaling) to a cluster Poisson process, which is similar to a Poisson process, but with several (random number) of events arriving clustered in time. The average number of events in a cluster defined by a given threshold is 1/ .…”

Section: The Distribution and The Clustering Of Fast Cmesmentioning

confidence: 99%

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Distribution and clustering of fast coronal mass ejections

2011

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[1] The purpose of this paper is to investigate the statistical properties of high-speed coronal mass ejections (fast CMEs), which play a major role in Space Weather. We study the cumulative distribution of the initial CME speeds applying a new, advanced statistical method based on the scaling properties of averages of maximal speeds selected in time intervals of fixed sizes. This method allows us for the first time to obtain a systematic statistical description of the fast CME speeds. Using this method, we identify a self-similar (power law) high-speed portion of the spectrum of the speed maxima in the range of speeds from about 700 km/s to 2000 km/s. This self-similar range of the speed distribution provides a meaningful definition of "the fast" CMEs and indicates that these CMEs are produced by a process that is the same across the range of scales. The investigation of the temporal behavior of the fast CME events indicates that the time intervals between fast CMEs are not independent, i.e., fast CMEs arrive in clusters. We characterize the fast CMEs clustering by the exponent called the extremal index, which is the inverse of the averaged number of CMEs per cluster. An independent correlation analysis of the tail of the CME distribution confirms and further quantifies the temporal dependence among the fast CME events. To illustrate the predictive capabilities of the method, we identify clusters in the time series of CMEs with speeds greater than 1000 km/s and calculate their statistical characteristics such as the size and duration of the clusters. The method used in this paper can be applied to many other extreme geophysical events.

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“…These estimates can be further justified by the asymptotic statistical theory of Hsing et al [1988].…”

Section: The Distribution and The Clustering Of Fast Cmesmentioning

confidence: 90%

Section: The Distribution and The Clustering Of Fast Cmesmentioning

confidence: 99%

Distribution and clustering of fast coronal mass ejections

2011

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“…We define the cluster size distribution, for each j ∈ N The next theorem gives the convergence of the REPP to a compound Poisson process under the assumptions ∆(u n ), the existence of a distributional limit for M n and the existence of limit of the cluster size distribution π n defined above. The statement is an adjustment of the content of [128,Theorem 4.2], having in mind that the REPP N n defined in (3.3.1) has a slightly different time rescaling when compared to the one used in [128]. Theorem 3.3.6.…”

Section: 33mentioning

confidence: 99%

Extremes and Recurrence in Dynamical Systems

Lucarini¹,

Faranda²,

Freitas³

et al. 2016

194

253

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ii 4.1.2 The New Conditions 44 4.1.3 The Existence of EVL for General Stationary Stochastic Processes under Weaker Hypotheses 46 4.1.4 Proofs of Theorem 4.1.4 and Corollary 4.1.5 48 4.2 Extreme Values for Dynamically Defined Stochastic Processes 53 4.2.1 Observables and Corresponding Extreme Value Laws 55 4.2.2 Extreme Value Laws for Uniformly Expanding Systems 59 4.2.3 Example 4.2.1 revisited 61 4.2.4 Proof of the Dichotomy for Uniformly Expanding Maps 63 4.3 Point Processes of Rare Events 64 4.3.1 Absence of Clustering 64 4.3.2 Presence of Clustering 65 4.3.3 Dichotomy for Uniformly Expanding Systems for Point Processes 67 4.4 Conditions Д q (u n ), D 3 (u n ), D p (u n ) * and Decay of Correlations 68 4.5 Specific Dynamical Systems where the Dichotomy Applies 71 4.5.1 Rychlik Systems 72 4.5.2 Piecewise Expanding Maps in Higher Dimensions 73 4.6 Extreme Value Laws for Physical Observables 74

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“…(3), and this is the same distribution as that of an arbitrary exceedance. For more details, see Leadbetter et al (1983), Hsing (1987), Hsing et al (1988), andLeadbetter (1991).…”

Section: H (Y)mentioning

confidence: 99%

Geostatistics of Dependent and Asymptotically Independent Extremes

2013

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Spatial modeling of rare events has obvious applications in the environmental sciences and is crucial when assessing the effects of catastrophic events (such as heatwaves or widespread flooding) on food security and on the sustainability of societal infrastructure. Although classical geostatistics is largely based on Gaussian processes and distributions, these are not appropriate for extremes, for which maxstable and related processes provide more suitable models. This paper provides a brief overview of current work on the statistics of spatial extremes, with an emphasis on the consequences of the assumption of max-stability. Applications to winter minimum temperatures and daily rainfall are described.

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On the exceedance point process for a stationary sequence

Cited by 228 publications

References 16 publications

Distribution and clustering of fast coronal mass ejections

Distribution and clustering of fast coronal mass ejections

Extremes and Recurrence in Dynamical Systems

Geostatistics of Dependent and Asymptotically Independent Extremes

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