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Summary: Count data are omnipresent in many applied fields, often with overdispersion. With mixtures of Poisson distributions representing an elegant and appealing modelling strategy, we focus here on how the tail behaviour of the mixing distribution is related to the tail of the resulting Poisson mixture. We define five sets of mixing distributions, and we identify for each case whenever the Poisson mixture is in, close to or far from a domain of attraction of maxima. We also characterize how the Poisson mixture behaves similarly to a standard Poisson distribution when the mixing distribution has a finite support. Finally, we study, both analytically and numerically, how goodness‐of‐fit can be assessed with the inspection of tail behaviour. [ABSTRACT FROM AUTHOR]

Summary: The topographical complexity of coral reefs is of primary importance for a number of hydrodynamical and ecological processes. The present study is based on a series of high‐resolution seabottom elevation measurements along the Maupiti Barrier Reef, French Polynesia. Several statistical metrics and spectral analysis are used to characterize the spatial evolution of the coral geometrical structure from the reef crest to the backreef. A consistent fractal‐like power law exists in the spectral density of bottom elevation for length scales between 0.1 and 7 m, while at larger scale, the reef structure shows a different pattern. Such a fine characterization of the reef geometrical structure provides key elements to reconstruct the reef history, to improve the representation of reef roughness in hydrodynamical models and to monitor the evolution of coral reef systems in the context of global change. © 2020 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

In atmospheric chemistry, daily maxima concentrations capture information about the variability among peak values. Statistically, they can often be modeled by a Gumbel distribution. This is the case for two very important greenhouse gases methane and nitrous oxide maxima when they are measured at our site of interest, Gif-sur-Yvette, a city south west of Paris. In practice, those two daily concentrations are not always recorded during the same period, and it would be of interest to reconstruct one from the other one. Such a type of inference can be handled within a state space modeling framework, but state space models are not tailored to represent the dynamics among Gumbel-distributed maxima. By building on our previous work, which made a link between linear autoregressive time series and Gumbel-distributed maxima, we propose and study such a state space model. It has the advantages of being linear and of preserving the Gumbel characteristic in both the state and observational equations. Concerning the inference of the hidden maxima at the state equation level, we derive the optimal weights of the auxiliary particle filtering approach of Pitt and Shephard. A simulation study indicates that our approach offers a gain over the Kalman filter, the bootstrap filter, and the nonmodified version of the Pitt and Shephard auxiliary filter. Copyright © 2012 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The article presents a study on autoregressive (AR) models for maxima and their applications to methane (CH4) and nitrous oxide ( N2O). The authors impose that AR models have to follow a Gumbel distribution whose main theoretical properties are derived. The study also offers a simple way to model short-term dependencies among maxima stemming.