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### ANOVA using commutative Jordan algebras, an application

Discussiones Mathematicae Probability and Statistics

Binary operations on commutative Jordan algebras are used to carry out the ANOVA of a two layer model. The treatments in the first layer nests those in the second layer, that being a sub-model for each treatment in the first layer. We present an application with data retried from agricultural experiments.

### Application of biregressional designs to electrodialytic removal of heavy metals from contaminated matrices

Discussiones Mathematicae Probability and Statistics

Given a base design with quantitative factors and a primary linear regression to each of the treatments, we may adjust secondary regressions of linear combinations of the adjusted coefficients on the primary regressions on the factor levels, thus obtaining a biregressional model. A biregressional design was established for a set of treatments, defined from quantitative factors and a linear regression in the same variables. Afterwards the action of the regression coefficients...

### Application of MCMC to change point detection

Applications of Mathematics

A nonstandard approach to change point estimation is presented in this paper. Three models with random coefficients and Bayesian approach are used for modelling the year average temperatures measured in Prague Klementinum. The posterior distribution of the change point and other parameters are estimated from the random samples generated by the combination of the Metropolis-Hastings algorithm and the Gibbs sampler.

### Bayesian methods in hydrology: a review.

RACSAM

Hydrology and water resources management are inherently affected by uncertainty in many of their involved processes, including inflows, rainfall, water demand, evaporation, etc. Statistics plays, therefore, an essential role in their study. We review here some recent advances within Bayesian statistics and decision analysis which will have a profound impact in these fields.

### Canonical non-symmetrical correspondence analysis: an alternative in constrained ordination.

SORT

Canonical non-symmetrical correspondence analysis is developed as an alternative method for constrained ordination, relating external information (e.g., environmental variables) with ecological data, considering species abundance as dependant on sites. Ordination axes are restricted to be linear combinations of the environmental variables, based on the information of the most abundant species. This extension and its associated unconstrained ordination method are terms of a global model that permits...

### Comparison of two common estimators of the ratio of the means of independent normal variables in agricultural research.

Journal of Applied Mathematics and Decision Sciences

### Covariance Structure of Principal Components for Three-Part Compositional Data

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates....

### Detecting atypical data in air pollution studies by using shorth intervals for regression

ESAIM: Probability and Statistics

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

### Detecting atypical data in air pollution studies by using shorth intervals for regression

ESAIM: Probability and Statistics

To validate pollution data, subject-matter experts in Airpl (an organization that maintains a network of air pollution monitoring stations in western France) daily perform visual examinations of the data and check their consistency. In this paper, we describe these visual examinations and propose a formalization for this problem. The examinations consist in comparisons of so-called shorth intervals so we build a statistical test that compares such intervals in a nonparametric regression model. This...

### Detekce změn v časových řadách a její aplikace v ekologii

Pokroky matematiky, fyziky a astronomie

### Development of the kriging method with application

Applications of Mathematics

This paper describes a modification of the kriging method for working with the square root transformation of a spatial random process. We have developed this method for the situation where the spatial process observed is not supposed to be stationary but the assumption is that its square root is a second order stationary spatial random process. Consequently this method is developed for estimating the integral of the process observed and finally some application of the method is given to data from...

### Dissection multi-échelle de quelques systèmes naturels : de la cryosphère Antarctique aux pulsations solaires

Annales de la faculté des sciences de Toulouse Mathématiques

L’objectif de cet article est d’illustrer la nature multi-échelle de quelques systèmes naturels en sciences de l’univers. Nous nous intéressons tout d’abord à l’onde circumpolaire Antarctique, une des manifestations les plus marquantes de la variabilité australe. Sa variabilité est analysée à partir de relevés de stations de météorologie côtières du continent Antarctique, fournissant des données de température depuis 1955. Grâce à une « décomposition modale empirique » (DME) couplée à une analyse...

### Drought models based on Burr XII variables

Applicationes Mathematicae

Burr distributions are some of the most versatile distributions in statistics. In this paper, a drought application is described by deriving the exact distributions of U = XY and W = X/(X+Y) when X and Y are independent Burr XII random variables. Drought data from the State of Nebraska are used.

### Estimating a resource selection function with line transect sampling.

Journal of Applied Mathematics and Decision Sciences

### Global correlation and uncertainty accounting

Dependence Modeling

For a high dimensional field of random variables, global correlation is defined as the ratio of average covariance and average variance, and its elementary properties are studied. Global correlation is used to harmonize uncertainty assessments at global and local scales. It can be estimated by the correlation of random aggregations of fixed size of disjoint sets of random variables. Illustrative applications are given using crop loss per county per year and forest carbon.

### Heavy tailed durations of regional rainfall

Applications of Mathematics

Durations of rain events and drought events over a given region provide important information about the water resources of the region. Of particular interest is the shape of upper tails of the probability distributions of such durations. Recent research suggests that the underlying probability distributions of such durations have heavy tails of hyperbolic type, across a wide range of spatial scales from 2 km to 120 km. These findings are based on radar measurements of spatially averaged rain rate...

### Modeling and forecasting the peak flows of a river.

Mathematical Problems in Engineering

### On the tail dependence in bivariate hydrological frequency analysis

Dependence Modeling

In Bivariate Frequency Analysis (BFA) of hydrological events, the study and quantification of the dependence between several variables of interest is commonly carried out through Pearson’s correlation (r), Kendall’s tau (τ) or Spearman’s rho (ρ). These measures provide an overall evaluation of the dependence. However, in BFA, the focus is on the extreme events which occur on the tail of the distribution. Therefore, these measures are not appropriate to quantify the dependence in the tail distribution....

### Sensitivity studies of pollutant concentrations calculated by the UNI-DEM with respect to the input emissions

Open Mathematics

The influence of emission levels on the concentrations of four important air pollutants (ammonia, ozone, ammonium sulphate and ammonium nitrate) over three European cities (Milan, Manchester, and Edinburgh) with different geographical locations is considered. Sensitivity analysis of the output of the Unified Danish Eulerian Model according to emission levels is provided. The Sobol’ variance-based approach for global sensitivity analysis has been applied to compute the corresponding sensitivity measures....

### SUR models applied to an environmental situation with missing data and censored values.

Journal of Applied Mathematics and Decision Sciences

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