Journal ArticleDOI
Extreme Value Distributions for the Skew-Symmetric Family of Distributions
Sheng Mao Chang,Marc G. Genton +1 more
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TLDR
In this paper, the extreme value distribution of the skew-symmetric family is derived, where the probability density function of the latter is defined as twice the product of a symmetric density and a skewing function.Abstract:
We derive the extreme value distribution of the skew-symmetric family, the probability density function of the latter being defined as twice the product of a symmetric density and a skewing function. We show that, under certain conditions on the skewing function, this extreme value distribution is the same as that for the symmetric density. We illustrate our results using various examples of skew-symmetric distributions as well as two data sets.read more
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Book
The Skew-Normal and Related Families
TL;DR: This comprehensive treatment, blending theory and practice, will be the standard resource for statisticians and applied researchers, and Assuming only basic knowledge of (non-measure-theoretic) probability and statistical inference, the book is accessible to the wide range of researchers who use statistical modelling techniques.
Journal ArticleDOI
Methods for generating families of univariate continuous distributions in the recent decades
TL;DR: In this paper, five general methods of combination and their variations are discussed: (1) method of generating skew distributions, (2) method adding parameters (e.g., exponentiation), (3) beta generated method, (4) transformed-transformer method, and (5) composite method.
Journal ArticleDOI
Multivariate extreme models based on underlying skew-t and skew-normal distributions
TL;DR: The limiting distribution of maxima of skew-t random vectors is derived for the first time and it is shown that its limiting case, as the degree of freedom goes to infinity, is the skewed version of the well-known Husler-Reiss model.
Journal ArticleDOI
Rates of convergence of extremes from skew-normal samples
TL;DR: For a skew-normal random sequence, the optimal convergence rate of the normalized maximum to the Gumbel extreme value distribution was shown to be 1 / log n in this article.
Journal ArticleDOI
Primordial non-Gaussianity and extreme-value statistics of galaxy clusters
TL;DR: In this paper, the authors present a solution to this problem using Extreme-Value Statistics, taking into account primordial non-Gaussianity and its effects on the abundance and the clustering of rare objects.
References
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Book
An Introduction to Statistical Modeling of Extreme Values
TL;DR: This paper presents a meta-modelling framework that automates the very labor-intensive and therefore time-heavy and therefore expensive and expensive process of manually cataloging and modeling extreme value values in sequences.
Book
Modelling Extremal Events: for Insurance and Finance
TL;DR: In this article, an approach to Extremes via Point Processes is presented, and statistical methods for Extremal Events are presented. But the approach is limited to time series analysis for heavy-tailed processes.
Journal ArticleDOI
An Introduction to Statistical Modeling of Extreme Values
TL;DR: In this article, an Introduction to Statistical Modeling of Extreme Values is presented, along with a discussion of statistical models of extreme values and their application in statistical modeling of extreme value.
Book
Extreme Values, Regular Variation, and Point Processes
TL;DR: In this paper, the authors present a survey of the main domains of attraction and norming constants in point processes and point processes, and their relationship with multivariate extremity processes.