Displaying similar documents to “Stability of a characterization of normal distributions based on the first two conditional moments.”

On a general structure of the bivariate FGM type distributions

Sayed Mohsen Mirhosseini, Mohammad Amini, Ali Dolati (2015)

Applications of Mathematics

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In this paper, we study a general structure for the so-called Farlie-Gumbel-Morgenstern (FGM) family of bivariate distributions. Through examples we show how to use the proposed structure to study dependence properties of the FGM type distributions by a general approach.

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

K. Müller, W.-D. Richter (2016)

Dependence Modeling

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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

K. Müller, W.-D. Richter (2017)

Dependence Modeling

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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...

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

K. Müller, W.-D. Richter (2016)

Dependence Modeling

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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...