Flood frequency estimation in New Zealand using a region of influence approach and statistical depth functions

2020 ◽  
Vol 589 ◽  
pp. 125187
Author(s):  
George A. Griffiths ◽  
Shailesh Kumar Singh ◽  
Alistair I. McKerchar
Keyword(s):  
New Zealand ◽  
Frequency Estimation ◽  
Flood Frequency ◽  
Statistical Depth ◽  
Depth Functions ◽  
Statistical Depth Functions

scholarly journals Depth classification based on affine-invariant, weighted and kernel-based spatial depth functions

2021 ◽  
Vol 48 (2) ◽  
Author(s):  
Olusola S. Makinde ◽  
Keyword(s):  
Affine Invariant ◽  
Classification Methods ◽  
Statistical Depth ◽  
Depth Functions ◽  
Maximal Depth ◽  
Depth Classification ◽  
Multivariate Outcomes ◽  
Statistical Depth Functions ◽  
Spatial Depth

Several multivariate depth functions have been proposed in the literature, of which some satisfy all the conditions for statistical depth functions while some do not. Spatial depth is known to be invariant to spherical and shift transformations. In this paper, the possibility of using different versions of spatial depth in classification is considered. The covariance-adjusted, weighted, and kernel-based versions of spatial depth functions are presented to classify multivariate outcomes. We extend the maximal depth classification notions for the covariance-adjusted, weighted, and kernel-based spatial depth versions. The classifiers' performance is considered and compared with some existing classification methods using simulated and real datasets.

scholarly journals Comparison-based centrality measures

2021 ◽  
Author(s):  
Luca Rendsburg ◽  
Damien Garreau
Keyword(s):  
Machine Learning ◽  
Learning Community ◽  
Outlier Detection ◽  
Centrality Measures ◽  
Human Intelligence ◽  
Ordinal Information ◽  
Statistical Depth ◽  
Depth Functions ◽  
Statistical Depth Functions ◽  
Synthetic Datasets

AbstractRecently, learning only from ordinal information of the type “item x is closer to item y than to item z” has received increasing attention in the machine learning community. Such triplet comparisons are particularly well suited for learning from crowdsourced human intelligence tasks, in which workers make statements about the relative distances in a triplet of items. In this paper, we systematically investigate comparison-based centrality measures on triplets and theoretically analyze their underlying Euclidean notion of centrality. Two such measures already appear in the literature under opposing approaches, and we propose a third measure, which is a natural compromise between these two. We further discuss their relation to statistical depth functions, which comprise desirable properties for centrality measures, and conclude with experiments on real and synthetic datasets for medoid estimation and outlier detection.

Application de la fonction bêta et des polynômes de Jacobi à l'analyse des valeurs extrêmes

1994 ◽  
Vol 21 (6) ◽  
pp. 1074-1080 ◽  
Author(s):  
J. Llamas ◽  
C. Diaz Delgado ◽  
M.-L. Lavertu
Keyword(s):  
Frequency Estimation ◽  
Probabilistic Method ◽  
Beta Function ◽  
Real Data ◽  
Flood Frequency ◽  
Data Series ◽  
Data Generation ◽  
Practical Applications ◽  
Flood Probability ◽  
Probable Maximum Flood

In this paper, an improved probabilistic method for flood analysis using the probable maximum flood, the beta function, and orthogonal Jacobi’s polynomials is proposed. The shape of the beta function depends on the sample's characteristics and the bounds of the phenomenon. On the other hand, a serial of Jacobi’s polynomials has been used improving the beta function and increasing its convergence degree toward the real flood probability density function. This mathematical model has been tested using a sample of 1000 generated beta random data. Finally, some practical applications with real data series, from important Quebec's rivers, have been performed; the model solutions for these rivers showed the accuracy of this new method in flood frequency estimation. Key words: probable maximum flood, beta function, orthogonal polynomials, distribution function, flood frequency estimation, data generation, convergency.

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