International audienc

extremefit is a package to estimate the extreme quantiles and probabilities of rare events. The idea of our approach is to adjust the tail of the distribution function over a threshold with a Pareto distribution. We propose a pointwise data driven procedure to choose the threshold. To illustrate the method, we use simulated data sets and three real-world data sets included in the package.

Water quality can be evaluated using biomarkers such as tissular enzymatic activities of endemic species. Measurement of molluscs bivalves activity at high frequency (e.g., valvometry) during a long time period is another way to record the animal behavior and to evaluate perturbations of the water quality in real time. As the pollution affects the activity of oysters, we consider the valves opening and closing velocities to monitor the water quality assessment. We propose to model the huge volume of velocity data collected in the framework of valvometry using a new nonparametric extreme values statistical model. The objective is to estimate the tail probabilities and the extreme quantiles of the distribution of valve closing velocity. The tail of the distribution function of valve closing velocity is modeled by a Pareto distribution with parameter 𝜃 t,τ , beyond a threshold τ according to the time t of the experiment. Our modeling approach reveals the dependence between the specific activity of two enzymatic biomarkers (Glutathione-S-transferase and acetylcholinesterase) and the continuous recording of oyster valve velocity, proving the suitability of this tool for water quality assessment. Thus, valvometry allows in real-time in situ analysis of the bivalves behavior and appears as an effective early warning tool in ecological risk assessment and marine environment monitoring.

Using the variance stabilizing technique, a product multinomial model is introduced to generate a new statistic to test observers' uncertainty in a weighted concordance analysis. Distance matrices which follow some specific rules are obtained by linear combinations of hierarchical distance matrices whose elements are equal to 0 or 1 and unit diagonal. The new statistic is compared with the kappa statistic interpreted by considering the covariance matrix generated by the data. By rewriting the test statistic in a barycentric form, one demonstrates how to modify the barycentric coefficients to derive an adequate measure of the interobserver agreement. The methods are illustrated using two examples.