In statistics, extreme events are often defined as excesses above a given large threshold. This definition allows hydrologists and flood planners to apply Extreme-Value Theory (EVT) to their time series of interest. Even in the stationary univariate context, this approach has at least two main drawbacks. First, working with excesses implies that a lot of observations (those below the chosen threshold) are completely disregarded. The range of precipitation is artificially shopped down into two pieces, namely large intensities and the rest, which necessarily imposes different statistical models for each piece. Second, this strategy raises a nontrivial and very practical difficultly: how to choose the optimal threshold which correctly discriminates between low and heavy rainfall intensities. To address these issues, we propose a statistical model in which EVT results apply not only to heavy, but also to low precipitation amounts (zeros excluded). Our model is in compliance with EVT on both ends of the spectrum and allows a smooth transition between the two tails, while keeping a low number of parameters. In terms of inference, we have implemented and tested two classical methods of estimation: likelihood maximization and probability weighed moments. Last but not least, there is no need to choose a threshold to define low and high excesses. The performance and flexibility of this approach are illustrated on simulated and hourly precipitation recorded in Lyon, France.
This study focuses on two main rivers of Bohemia (Czech Republic): the Vltava and the Elbe. Flows are determined for the Elbe at Děčín (discharges) and Litoměřice (water stages), and for the Vltava at Prague (discharges). Extreme flows have an important socio-economic impact; hence modelling their occurrence accurately is crucial. We identify the meteorological causes for floods: (a) the winter type due to snowmelt, ice damming, and usually rain, and (b) the summer type due to continuous heavy rains. The amplitude and frequency of floods are analysed using extreme value theory, in a non-stationary context. This allows the determination of the trends of flood features during the instrumental period and their dependence on atmospheric circulation patterns.Key words Bohemia; floods; generalized extreme value theory; peak over threshold; return level; Elbe River; Vltava River
Analyse statistique des crues en Bohême (République Tchèque) depuis 1825Résumé Cette étude traite des deux rivières principales de Bohême (République Tchèque): la Rivière Vltava et la Rivière Elbe. Les mesures sont effectuées à Děčín (débits) et à Litoměřice (niveaux d'eau) pour la Rivière Elbe, et à Prague (débits) pour la Vltava. Les débits extrêmes ont un important impact socio-économique, et la prévision de leurs occurrences et ordres de grandeur est donc cruciale. Nous identifions deux causes météorologiques pour les crues: (a) celles d'hiver sont causées par la fonte des neiges, les embâcles de glace et les pluies, et (b) celles d'été sont dues à des pluies intenses et continues. L'amplitude et la fréquence de ces crues sont analysées dans le cadre de la théorie statistique des valeurs extrêmes non-stationnaire. Ceci nous a permis de détecter les tendances des caractéristiques des crues depuis le début de la période instrumentale et leur dépendance aux types de circulation atmosphérique.
Abstract.Since the pioneering work of Landwehr et al. (1979), Hosking et al. (1985) and their collaborators, the Probability Weighted Moments (PWM) method has been very popular, simple and efficient to estimate the parameters of the Generalized Extreme Value (GEV) distribution when modeling the distribution of maxima (e.g., annual maxima of precipitations) in the Identically and Independently Distributed (IID) context. When the IID assumption is not satisfied, a flexible alternative, the Maximum Likelihood Estimation (MLE) approach offers an elegant way to handle nonstationarities by letting the GEV parameters to be time dependent. Despite its qualities, the MLE applied to the GEV distribution does not always provide accurate return level estimates, especially for small sample sizes or heavy tails. These drawbacks are particularly true in some non-stationary situations. To reduce these negative effects, we propose to extend the PWM method to a more general framework that enables us to model temporal covariates and provide accurate GEV-based return levels. Theoretical properties of our estimators are discussed. Small and moderate sample sizes simulations in a non-stationary context are analyzed and two brief applications to annual maxima of CO 2 and seasonal maxima of cumulated daily precipitations are presented.
Four cases of acute nonlymphocytic leukemia with primitive basophilic differentiation are presented. In all four cases, study revealed Philadelphia chromosome negativity, and in none were there clinical findings of chronic granulocytic leukemia. In each case, the leukemic blasts contained granules that failed to stain for peroxidase content but stained positively with toluidine blue. The former result could have led to the misclassification of the cases as lymphoid leukemias. Three of the four patients had physical findings that may have been due to circulating histamine excess. The histochemical and clinical features of these cases suggest that certain examples of leukemia with basophilic differentiation represent a distinctive variant of acute nonlymphocytic leukemia.
Of 50 consecutive patients (30 female and 20 male; median age,70 years) with a myeloproliferative disorder and a 5q- chromosome, 12 (24%) had refractory anemia, 16 (32%) had refractory anemia with excess blasts, 13 (26%) had acute nonlymphocytic leukemia, six (12%) had the 5q- syndrome, and three (6%) had an unclassifiable myeloproliferative disease. Twenty-five patients had only a 5q- anomaly (group 1), and 25 had a 5q- plus additional chromosome abnormalities (group 2). Four types of 5q- anomalies were recognized: a del(5)(q13q33) occurred in 39 patients, a del(5)(q31q35) in nine, a del(5)(q22q33) in one, and a del(5)(q13q35) in one. The survival distribution for patients in group 1 was significantly better (P = .012) than for those in group 2. Cox- model analyses indicated that having a 5q- chromosome and other abnormalities is significantly (P less than .01) associated with poor survival even after adjustment for the effects of other important factors such as type of disease, age, and sex. The two groups had similar distributions of most variables, including age, sex, and disease types. However, patients in group 1 had a significantly higher platelet count and mean corpuscular volume than those in group 2. Only two patients in group 1 had had prior chemotherapy, but nine in group 2 had had either prior chemotherapy or radiation or both, and one patient in group 2 had had heavy exposure to pesticides.
Following the work of Azzalini ([2] and [3]) on the skew normal distribution, we propose an extension of the Generalized Extreme Value (GEV) distribution, the SGEV. This new distribution allows for a better fit of maxima and can be interpreted as both the distribution of maxima when maxima are taken on dependent data and when maxima are taken over a random block size. We propose to estimate the parameters of the SGEV distribution via the Probability Weighted Moments method. A simulation study is presented to provide an application of the SGEV on block maxima procedure and return level estimation. The proposed method is also implemented on a real-life data.
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