Heavy-Tailed Distributions: Properties and Tests

Bryson, Maurice C.

doi:10.1080/00401706.1974.10489150

Cited by 165 publications

(37 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is a suitable model for components that age with time. Bryson (1974) has argued that Lomax provides a very good alternative to common life time distributions i.e. exponential, Weibull, or gamma distributions when the experimenter presumes that the population distribution may be heavy tailed.…”

Section: Introductionmentioning

confidence: 99%

On Inference of Overlapping Coefficients in TwoLomaxPopulations Using Different Sampling Methods

Helu

Samawi

2011

Journal of Statistical Theory and Practice

View full text Add to dashboard Cite

This paper investigates point and interval estimation for some well-known measures of overlap. Two types of sampling procedures, namely, Simple Random Sample and Ranked Set Sample from two Lomax populations with different shape parameters are considered. Simulation studies are conducted to get insight on the performance of the proposed estimators. Taylor series approximations as well as bootstrap method are used to construct confidence intervals for those measures.

show abstract

Section: Introductionmentioning

confidence: 99%

On Inference of Overlapping Coefficients in TwoLomaxPopulations Using Different Sampling Methods

Helu

Samawi

2011

Journal of Statistical Theory and Practice

View full text Add to dashboard Cite

show abstract

“…We observe that the KS score is quite low for the first three hours, indicating that 12. Other options include the Berk-Jones test, the score test and their integrated versions [19], [20]. our GPDCM predicts accurate near-term traffic distributions.…”

Section: Resultsmentioning

confidence: 99%

Non-Myopic Adaptive Route Planning in Uncertain Congestion Environments

Liu

Yue

Krishnan

2015

IEEE Trans. Knowl. Data Eng.

View full text Add to dashboard Cite

We consider the problem of adaptively routing a fleet of cooperative vehicles within a road network in the presence of uncertain and dynamic congestion conditions. To tackle this problem, we first propose a Gaussian Process Dynamic Congestion Model that can effectively characterize both the dynamics and the uncertainty of congestion conditions. Our model is efficient and thus facilitates real-time adaptive routing in the face of uncertainty. Using this congestion model, we develop efficient algorithms for nonmyopic adaptive routing to minimize the collective travel time of all vehicles in the system. A key property of our approach is the ability to efficiently reason about the long-term value of exploration, which enables collectively balancing the exploration/exploitation trade-off for entire fleets of vehicles. Our approach is validated by traffic data from two large Asian cities. Our congestion model is shown to be effective in modeling dynamic congestion conditions. Our routing algorithms also generate significantly faster routes compared to standard baselines, and achieve near-optimal performance compared to an omniscient routing algorithm. We also present the results from a preliminary field study, which showcases the efficacy of our approach.

show abstract

“…12, it was necessary first to check the assumption of exponential-like upper tail for the probability distribution of 8-day rainfall volumes. This has been performed with the aid of the conditional mean exceedance (CME) function, denoted by M(u), the definition of which, according to Bryson (1974), is given by…”

Section: Foundations Of the Gradex Methodsmentioning

confidence: 99%

Investigation on the properties of the relationship between rare and extreme rainfall and flood volumes, under some distributional restrictions

Naghettini

Gontijo²,

Portela

2011

Stoch Environ Res Risk Assess

View full text Add to dashboard Cite

The fact that rainfall data are usually more abundant and more readily regionalized than streamflow data has motivated hydrologists to conceive methods that incorporate the hydrometeorologial information into flood frequency analyses. Some of them, particularly those derived from the French GRADEX method, involve assumptions concerning the relationship between extreme rainfall and flood volumes, under some distributional restrictions. In particular, for rainfall probability distributions exhibiting exponential-like upper tails, it is possible to derive the shape and scale of the probability distribution of flood volumes by hypothesizing the basic properties of such a relationship, under rare and/or extreme conditions. This paper focuses on a parametric mathematical model for the relationship between rare and extreme rainfall and flood volumes under exponentially-tailed distributions. The model is analyzed and fitted to rare and extreme events derived from hydrological simulation of long stochastically-generated synthetic series of rainfall and evaporation for the Indaiá River basin, located in south-central Brazil. The paper also provides a sensitivity analysis of the model parameters in order to better understand flood events under rare and extreme conditions. By working with hydrologically plausible hypothetical events, the modeling approach proved to be a useful way to explore extraordinary rainfall and flood events. The results from this exploratory analysis provide grounds to derive some conclusions regarding the relative positions of the upper tails of the probability distributions of rainfall and flood volumes.

show abstract

Heavy-Tailed Distributions: Properties and Tests

Cited by 165 publications

References 11 publications

On Inference of Overlapping Coefficients in TwoLomaxPopulations Using Different Sampling Methods

On Inference of Overlapping Coefficients in TwoLomaxPopulations Using Different Sampling Methods

Non-Myopic Adaptive Route Planning in Uncertain Congestion Environments

Investigation on the properties of the relationship between rare and extreme rainfall and flood volumes, under some distributional restrictions

Contact Info

Product

Resources

About