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A statistical analysis of water quality data collected on paired agricultural watersheds was undertaken. The objective of the study was to evaluate trends in water quality. The data sets that were used to determine the changes in water quality were taken from the project "Gestion de leau dans le bassin versant de la partie superieure du ruisseau St. Esprit". For the period from 1994 to 1996, the analysed water quality parameter were nitrate, phosphate, ammonium, potassium, total Kjeldahl nitrogen, total phosphorus and suspended sediment. / The data sets were analysed using descriptive statistics, graphical techniques and non-parametric methods to detect trends in the measured water quality parameters. The statistical analyses were undertaken to determine the effects of soil conservation practices and fertiliser management and to compare different sampling strategies. / The analyses showed that there were no detectable changes in water quality over the 3-year period related to the conservation practices. The lack of improvement in water quality might be due to the slow rate of adoption of conservation practices and to climatic variations. / For the non-parametric methods applied, it was possible to show that climatic variations on small watershed affect the results over a short time period (<5 years). The phosphate concentration on the control showed a significant upward trend. The nitrate concentration on St. Esprit showed an upward trend over the 3-year period and then downward trend after a 4-year period of water quality data. This was likely due to the implementation of best management practices. / The statistical analyses showed that weekly sampling on fixed schedule produce the same results as automated sampling based upon flow rate related to a defined discharge. This shows that the more complex and expensive flow weighted sampling scheme is not required to detect trends in water quality.

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This thesis focuses on construction, properties and estimation of asymmetric heavy-tailed distributions, as well as on their applications to financial modeling and risk measurement. First of all, we suggest a general procedure to construct a fully asymmetric distribution based on a symmetrically parametric distribution, and establish some natural relationships between the symmetric and asymmetric distributions. Then, three new classes of asymmetric distributions are proposed by using the procedure: the Asymmetric Exponential Power Distributions (AEPD), the Asymmetric Student-t Distributions (ASTD) and the Asymmetric Generalized t Distribution (AGTD). For the first two distributions, we give an interpretation of their parameters and explore basic properties of them, including moments, expected shortfall, characterization by the maximum entropy property, and the stochastic representation. Although neither distribution satisfies the regularity conditions under which the ML estimators have the usual asymptotics, due to a non-differentiable likelihood function, we nonetheless establish asymptotics for the full MLE of the parameters. A closed-form expression for the Fisher information matrix is derived, and Monte Carlo studies are provided. We also illustrate the usefulness of the GARCH-type models with the AEPD and ASTD innovations in the context of predicting downside market risk of financial assets and demonstrate their superiority over skew-normal and skew-Student's t GARCH models. Finally, two new classes of generalized extreme value distributions, which include Jenkinson's GEV (Generalized Extreme Value) distribution (Jenkinson, 1955) as special cases, are proposed by using the maximum entropy principle, and their properties are investigated in detail.