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Czasopisma help

  1. 3 Dependence Modeling

Autorzy help

  1. 3 Müller K.

  2. 3 Richter W.-D.

Lata help

  1. 1 2017

  2. 2 2016

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Extreme value distributions for dependent jointly ln,p-symmetrically distributed random variables

100%
Müller K., Richter W.-D.
Dependence Modeling
|
2016
|
tom 4
|
nr 1
EN
A measure-of-cone representation of skewed continuous ln,p-symmetric distributions, n ∈ N, p > 0, is proved following the geometric approach known for elliptically contoured distributions. On this basis, distributions of extreme values of n dependent random variables are derived if the latter follow a joint continuous ln,p-symmetric distribution. Light, heavy, and extremely far tails as well as tail indices are discussed, and new parameters of multivariate tail behavior are introduced.
2
Content available remote

Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}

100%
Müller K., Richter W.-D.
Dependence Modeling
|
2016
|
tom 4
|
nr 1
EN
Integral representations of the exact distributions of order statistics are derived in a geometric way when three or four random variables depend on each other as the components of continuous ln,psymmetrically distributed random vectors do, n ∈ {3,4}, p > 0. Once the representations are implemented in a computer program, it is easy to change the density generator of the ln,p-symmetric distribution with another one for newly evaluating the distribution of interest. For two groups of stock exchange index residuals, maximum distributions are compared under dependence and independence modeling.
3
Content available remote

Exact distributions of order statistics from ln,p-symmetric sample distributions

100%
Müller K., Richter W.-D.
Dependence Modeling
|
2017
|
tom 5
|
nr 1
221-245
EN
We derive the exact distributions of order statistics from a finite number of, in general, dependent random variables following a joint ln,p-symmetric distribution. To this end,we first review the special cases of order statistics fromspherical aswell as from p-generalized Gaussian sample distributions from the literature. To study the case of general ln,p-dependence, we use both single-out and cone decompositions of the events in the sample space that correspond to the cumulative distribution function of the kth order statistic if they are measured by the ln,p-symmetric probability measure.We show that in each case distributions of the order statistics from ln,p-symmetric sample distribution can be represented as mixtures of skewed ln−ν,p-symmetric distributions, ν ∈ {1, . . . , n − 1}.
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