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Sharp equivalence between ρ- and τ-mixing coefficients

Rémi Peyre (2013)

Studia Mathematica

For two σ-algebras 𝓐 and ℬ, the ρ-mixing coefficient ρ(𝓐,ℬ) between 𝓐 and ℬ is the supremum correlation between two real random variables X and Y which are 𝓐 - resp. ℬ-measurable; the τ'(𝓐,ℬ) coefficient is defined similarly, but restricting to the case where X and Y are indicator functions. It has been known for a long time that the bound ρ ≤ Cτ'(1 + en | log τ'|) holds for some constant C; in this article, we show that C = 1 works and is best possible.

Shuffles of Min.

Piotr Mikusinski, Howard Sherwood, Michael D. Taylor (1992)

Stochastica

Copulas are functions which join the margins to produce a joint distribution function. A special class of copulas called shuffles of Min is shown to be dense in the collection of all copulas. Each shuffle of Min is interpreted probabilistically. Using the above-mentioned results, it is proved that the joint distribution of any two continuously distributed random variables X and Y can be approximated uniformly, arbitrarily closely by the joint distribution of another pair X* and Y* each of which...

Some results envolving the concepts of moment generating function and affinity between distribution functions. Extension for r k-dimensional normal distribution functions.

Antonio Dorival Campos (1999)

Qüestiió

We present a function ρ (F1, F2, t) which contains Matusita's affinity and expresses the affinity between moment generating functions. An interesting results is expressed through decomposition of this affinity ρ (F1, F2, t) when the functions considered are k-dimensional normal distributions. The same decomposition remains true for other families of distribution functions. Generalizations of these results are also presented.

Statistical aspects of associativity for copulas

José M. González-Barrios (2010)

Kybernetika

In this paper we study in detail the associativity property of the discrete copulas. We observe the connection between discrete copulas and the empirical copulas, and then we propose a statistic that indicates when an empirical copula is associative and obtain its main statistical properties under independence. We also obtained asymptotic results of the proposed statistic. Finally, we study the associativity statistic under different copulas and we include some final remarks about associativity...

Symmetries of random discrete copulas

Arturo Erdely, José M. González–Barrios, Roger B. Nelsen (2008)

Kybernetika

In this paper we analyze some properties of the discrete copulas in terms of permutations. We observe the connection between discrete copulas and the empirical copulas, and then we analyze a statistic that indicates when the discrete copula is symmetric and obtain its main statistical properties under independence. The results obtained are useful in designing a nonparametric test for symmetry of copulas.

The importance of being the upper bound in the bivariate family.

Carles M. Cuadras (2006)

SORT

Any bivariate cdf is bounded by the Fréchet-Hoeffding lower and upper bounds. We illustrate the importance of the upper bound in several ways. Any bivariate distribution can be written in terms of this bound, which is implicit in logit analysis and the Lorenz curve, and can be used in goodness-of-fit assesment. Any random variable can be expanded in terms of some functions related to this bound. The Bayes approach in comparing two proportions can be presented as the problem of choosing a parametric...

Weakly stationary processes with non–positive autocorrelations

Šárka Došlá, Jiří Anděl (2010)

Kybernetika

We deal with real weakly stationary processes { X t , t ∈ ℤ } with non-positive autocorrelations { r k } , i. e. it is assumed that r k ≤ 0 for all k = 1 , 2 , ⋯ . We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies r k ≤ 0 for all k = 1 , 2 , ⋯ are provided as well.

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