A hybrid Pareto model for asymmetric fat-tailed data: the univariate case

Carreau, Julie; Bengio, Yoshua

doi:10.1007/s10687-008-0068-0

Cited by 88 publications

(74 citation statements)

References 24 publications

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“…One component of the mixture was a light-tailed parametric density -which they took to be a Weibull density -whereas the other component was a GPD with a positive shape parameter ξ > 0. Carreau and Bengio (2006) proposed a more flexible mixture model in the context of conditional density estimation. In contrast to the Frigessi et al (2002) model, the number of components was not fixed a priori and each component was a hybrid Pareto distribution, defined as a Gaussian distribution whose upper-right tail was replaced by a heavy-tailed GPD.…”

Section: A Few Basic Conceptsmentioning

confidence: 99%

Extreme events: dynamics, statistics and prediction

Ghil

Yiou

Hallegatte

et al. 2011

Nonlin. Processes Geophys.

228

167

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Abstract. We review work on extreme events, their causes and consequences, by a group of European and American researchers involved in a three-year project on these topics. The review covers theoretical aspects of time series analysis and of extreme value theory, as well as of the deterministic modeling of extreme events, via continuous and discrete dynamic models. The applications include climatic, seismic and socio-economic events, along with their prediction.Two important results refer to (i) the complementarity of spectral analysis of a time series in terms of the continuous and the discrete part of its power spectrum; and (ii) the need for coupled modeling of natural and socio-economic systems. Both these results have implications for the study and prediction of natural hazards and their human impacts.

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Section: A Few Basic Conceptsmentioning

confidence: 99%

Extreme events: dynamics, statistics and prediction

Ghil

Yiou

Hallegatte

et al. 2011

Nonlin. Processes Geophys.

228

167

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“…Other univariate mixture models that take into account the EVT exist. Carreau and Bengio (2006) investigated a model that combines a non-parametric approach (neural networks) with EVT densities. The research developed therein can be viewed as an extension of these past approaches.…”

Section: Introductionmentioning

confidence: 99%

Modeling pairwise dependencies in precipitation intensities

Vrac

Naveau

Drobinski

2007

Nonlin. Processes Geophys.

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Abstract. In statistics, extreme events are classically defined as maxima over a block length (e.g. annual maxima of daily precipitation) or as exceedances above a given large threshold. These definitions allow the hydrologist and the flood planner to apply the univariate Extreme Value Theory (EVT) to their time series of interest. But these strategies have two main drawbacks. Firstly, working with maxima or exceedances implies that a lot of observations (those below the chosen threshold or the maximum) are completely disregarded. Secondly, this univariate modeling does not take into account the spatial dependence. Nearby weather stations are considered independent, although their recordings can show otherwise.To start addressing these two issues, we propose a new statistical bivariate model that takes advantages of the recent advances in multivariate EVT. Our model can be viewed as an extension of the non-homogeneous univariate mixture. The two strong points of this latter model are its capacity at modeling the entire range of precipitation (and not only the largest values) and the absence of an arbitrarily fixed large threshold to define exceedances. Here, we adapt this mixture and broaden it to the joint modeling of bivariate precipitation recordings. The performance and flexibility of this new model are illustrated on simulated and real precipitation data.

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“…The normal-normal model performs well for small sample sizes and low risk values if the data is in fact normally distributed (Jacobs et al, 2015a). The normal distribution, however, is light-tailed (Carreau and Bengio, 2008). Light tails can cause underestimation of the risk.…”

Section: Then the Pdf Of R Is Given By F Rmentioning

confidence: 99%

“…When ξ < 0, the distribution has a finite tail (e.g. beta and uniform distributions) (Carreau and Bengio, 2008). The tail index is a parameter that can be estimated by fitting a gpd to data.…”

Section: Then the Pdf Of R Is Given By F Rmentioning

confidence: 99%

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Statistical modelling of variability and uncertainty in risk assessment of nanoparticles

Jacobs

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Engineered nanoparticles (ENPs) are used everywhere and have large technological and economic potential. Like all novel materials, however, ENPs have no history of safe use.Insight into risks of nanotechnology and the use of nanoparticles is an essential condition for the societal acceptance and safe use of nanotechnology.Risk assessment of ENPs has been hampered by lack of knowledge about ENPs, their environmental fate, toxicity, testing considerations, characterisation of nanoparticles and human and environmental exposures and routes. This lack of knowledge results in uncertainty in the risk assessment. Moreover, due to the novelty of nanotechnology, risk assessors are often confronted with small samples of data on which to perform a risk assessment. Dealing with this uncertainty and the small sample sizes are main challenges when it comes to risk assessment of ENPs. The objectives of this thesis are (i) to perform a transparent risk assessment of nanoparticles in the face of large uncertainty in such a way that it can guide future research to reduce the uncertainty and (ii) to evaluate empirical and parametric methods to estimate the risk probability in the case of small sample sizes.To address the first objective, I adapted an existing Integrated Probabilistic Risk Assessment (IPRA) method for use in nanoparticle risk assessment. In IPRA, statistical distributions and bootstrap methods are used to quantify uncertainty and variability in the risk assessment in a two-dimensional Monte Carlo algorithm. This method was applied in a human health (nanosilica in food) and an environmental (nanoT iO 2 in water) risk context. I showed that IPRA leads to a more transparent risk assessment and can direct further environmental and toxicological research to the areas in which it is most needed.For the second objective, I addressed the problem of small sample size of the critical effect concentration (CEC) in the estimation of R = P (E xpC > C EC ), where E xpC is the exposure concentration. First I assumed normality and investigated various parametric and non-parametric estimators. I found that, compared to the non-parametric estimators, the parametric estimators enable us to better estimate and bound the risk when sample sizes and/or small risks are small. Moreover, the Bayesian estimator out-ABSTRACT performed the maximum likelihood estimators in terms of coverage and interval lengths.Second, I relaxed the normality assumption for the tails of the exposure and effect distributions. I developed a mixture model to estimate the risk, R = P (E xpC > C EC ), with the assumption of a normal distribution for the bulk data and generalised Pareto distributions for the tails. A sensitivity analysis showed significant influence of the tail heaviness on the risk probability, R, especially for low risks.In conclusion, to really be able to focus the research into the risks of ENPs to the most needed areas, probabilistic methods as used and developed in this thesis need to be implemented on a larger scale. With these methods,...

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A hybrid Pareto model for asymmetric fat-tailed data: the univariate case

Cited by 88 publications

References 24 publications

Extreme events: dynamics, statistics and prediction

Extreme events: dynamics, statistics and prediction

Modeling pairwise dependencies in precipitation intensities

Statistical modelling of variability and uncertainty in risk assessment of nanoparticles

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