Discretization of distributions in the maximum domain of attraction

Shimura, Takaaki

doi:10.1007/s10687-011-0137-7

Cited by 21 publications

(34 citation statements)

References 15 publications

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“…The GPD has an asymptotic justification for its form given by limit results of Pickands (1971) as the threshold tends to the upper endpoint of the distribution. Similar limit results hold for discrete random variables (Anderson, 1970(Anderson, , 1980Shimura, 2012) but these only hold for ξ ≥ 0 and are unable to provide non-degenerate limits for the Poisson distribution as the tail decays too quickly. Thus, these limit results do not provide flexible tail models for discrete random variables above non-limit thresholds.…”

Section: Extremal Mixture Modellingmentioning

confidence: 90%

Extreme value modelling of water-related insurance claims

Rohrbeck¹,

Eastoe

Frigessi

et al. 2018

Ann. Appl. Stat.

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snow-melt, and the number of water-related property insurance claims. Weather events which cause severe damages are of general interest, decision makers want to take efficient actions against them while the insurance companies want to set adequate premiums. The modelling is challenging since the underlying dynamics vary across geographical regions due to differences in topology, construction designs and climate. We develop new methodology to improve the existing models which fail to model high numbers of claims. The statistical framework is based on both mixture and extremal mixture modelling, with the latter being based on a discretized generalized Pareto distribution. Furthermore, we propose a temporal clustering algorithm and derive new covariates which lead to a better understanding of the association between claims and weather events. The modelling of the claims, conditional on the locally observed weather events, both fits the marginal distributions well and captures the spatial dependence between locations. Our methodology is applied to three cities across Norway to demonstrate its benefits.

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Section: Extremal Mixture Modellingmentioning

confidence: 90%

Extreme value modelling of water-related insurance claims

Rohrbeck¹,

Eastoe

Frigessi

et al. 2018

Ann. Appl. Stat.

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“…Finally, we consider the MDA hypothesis: This requirement has no direct correlation with hardware or software features, it is rather a statistical property. From previous statistical works, it is known that most of all continuous distributions satisfy this hypothesis, provided that the measurements are correctly acquired [61]. During the real measurements of our system, we clearly need to discretize the elapsed time.…”

Section: The Mda Hypothesismentioning

confidence: 98%

Timing Predictability in High-Performance Computing With Probabilistic Real-Time

2020

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Application requirements in High-Performance Computing (HPC) are becoming increasingly exacting, and the demand for computational resources is rising. In parallel, new application domains are emerging, as well as additional requirements, such as meeting real-time constraints. This requirement, typical of embedded systems, is difficult to guarantee when dealing with HPC infrastructures, due to the intrinsic complexity of the system. Traditional embedded systems static analyses to estimate the Worst-Case Execution Time (WCET) are not applicable to HPC, because modeling and analyzing all the system's hardware and software components is not practical. Measurement-based probabilistic analyses for the WCET emerged in the last decade to overcome these issues, but it requires the system to satisfy certain conditions to estimate a correct and safe WCET. In this work, we show the emerging application timing requirements, and we propose to exploit the probabilistic real-time theory to achieve the required time predictability. After a brief recap of the fundamentals of this methodology, we focus on its applicability to HPC systems, to check their ability to satisfy such conditions. In particular, we studied the advantages of having heterogeneous processors in HPC nodes and how resource management affects the applicability of the proposed technique.

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“…As shown in the numerical results section, the assumption of Lg > 10 is indeed a reasonable assumption since it reflects parametric values of practical interest. Insightfully, the latter distribution belongs to the MDA of Gumbel distribution and is uniquely recovered therein[12, Thm. 5].…”

mentioning

confidence: 94%

“…belongs to the maximum domain of attraction (MDA) of one of the three possible distribution types; namely the Gumbel, Fréchet or Weibull. According to[12, Thm. 3], the Poisson distribution is recoverable 3 in the MDA of Gumbel distribution yet not uniquely recovered.…”

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confidence: 99%

Extreme Age of Information for Wireless-Powered Communication Systems

Miridakis¹,

Zheng²,

Tsiftsis³

et al. 2022

Preprint

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The extreme or maximum age of information (AoI) is analytically studied for wireless communication systems. In particular, a wireless powered single-antenna source node and a receiver (connected to the power grid) equipped with multiple antennas are considered when operated under independent Rayleigh-faded channels. Via the extreme value theory and its corresponding statistical features, we demonstrate that the extreme AoI converges to the Gumbel distribution whereas its corresponding parameters are obtained in straightforward closed-form expressions. Capitalizing on this result, the risk of the extreme AoI realization is analytically evaluated according to some relevant performance metrics, while some useful engineering insights are manifested. Index TermsAge of information (AoI), extreme value theory, low-latency, wireless power transfer. I. INTRODUCTIONAge of information (AoI) represents an insightful performance metric for wireless communication systems, which indicates the timeliness of data delivery. Doing so, it has numerous applications in a set of various recent and upcoming real-time networking paradigms, e.g., Internet-of-things, vehicular and machine-type communications, healthcare, infrastructure and

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Discretization of distributions in the maximum domain of attraction

Cited by 21 publications

References 15 publications

Extreme value modelling of water-related insurance claims

Extreme value modelling of water-related insurance claims

Timing Predictability in High-Performance Computing With Probabilistic Real-Time

Extreme Age of Information for Wireless-Powered Communication Systems

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