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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

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.

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

88%

Müller K., Richter W.-D.

Dependence Modeling

2017

tom 5

nr 1

221-245

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}.

Ograniczanie wyników

2 Dependence Modeling

2 Müller K.

2 Richter W.-D.

1 2017

1 2016

Wyniki wyszukiwania

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

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