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A Biconvex Form for Copulas

Sebastian Fuchs (2016)

Dependence Modeling

We study the integration of a copula with respect to the probability measure generated by another copula. To this end, we consider the map [. , .] : C × C → R given by [...] where C denotes the collection of all d–dimensional copulas and QD denotes the probability measures associated with the copula D. Specifically, this is of interest since several measures of concordance such as Kendall’s tau, Spearman’s rho and Gini’s gamma can be expressed in terms of the map [. , .]. Quite generally, the map...

A copula test space model how to avoid the wrong copula choice

Frederik Michiels, Ann De Schepper (2008)


We introduce and discuss the test space problem as a part of the whole copula fitting process. In particular, we explain how an efficient copula test space can be constructed by taking into account information about the existing dependence, and we present a complete overview of bivariate test spaces for all possible situations. The practical use will be illustrated by means of a numerical application based on an illustrative portfolio containing the S&P 500 Composite Index, the JP Morgan Government...

A generalized bivariate lifetime distribution based on parallel-series structures

Vahideh Mohtashami-Borzadaran, Mohammad Amini, Jafar Ahmadi (2019)


In this paper, a generalized bivariate lifetime distribution is introduced. This new model is constructed based on a dependent model consisting of two parallel-series systems which have a random number of parallel subsystems with fixed components connected in series. The probability that one system fails before the other one is measured by using competing risks. Using the extreme-value copulas, the dependence structure of the proposed model is studied. Kendall's tau, Spearman's rho and tail dependences...

A nonparametric test of zero intrapair correlation

Antonín Lukš (1983)

Aplikace matematiky

The author applies the test criterion of P. Rothety to the statistical analysis of the positive correclation of symmetric pairs of observations. In this particular case he arrives at some new results. His work ends with a general proof of the consistency of Rothery's test.

A note on order statistics from symmetrically distributed samples

Marek Kałuszka, Andrzej Okolewski (2011)

Applicationes Mathematicae

We present a first moment distribution-free bound on expected values of L-statistics as well as properties of some numerical characteristics of order statistics, in the case when the observations are possibly dependent symmetrically distributed about the common mean. An actuarial interpretation of the presented bound is indicated.

A note on the Galambos copula and its associated Bernstein function

Jan-Frederik Mai (2014)

Dependence Modeling

There is an infinite exchangeable sequence of random variables {Xk}k∈ℕ such that each finitedimensional distribution follows a min-stable multivariate exponential law with Galambos survival copula, named after [7]. A recent result of [15] implies the existence of a unique Bernstein function Ψ associated with {Xk}k∈ℕ via the relation Ψ(d) = exponential rate of the minimum of d members of {Xk}k∈ℕ. The present note provides the Lévy–Khinchin representation for this Bernstein function and explores some...

A short note on multivariate dependence modeling

Vladislav Bína, Radim Jiroušek (2013)


As said by Mareš and Mesiar, necessity of aggregation of complex real inputs appears almost in any field dealing with observed (measured) real quantities (see the citation below). For aggregation of probability distributions Sklar designed his copulas as early as in 1959. But surprisingly, since that time only a very few literature have appeared dealing with possibility to aggregate several different pairwise dependencies into one multivariate copula. In the present paper this problem is tackled...

A subcopula based dependence measure

Arturo Erdely (2017)


A dependence measure for arbitrary type pairs of random variables is proposed and analyzed, which in the particular case where both random variables are continuous turns out to be a concordance measure. Also, a sample version of the proposed dependence measure based on the empirical subcopula is provided, along with an R package to perform the corresponding calculations.

Affinity between complex distribution functions.

Antonio Dorival Campos (1987)

Trabajos de Estadística

By analogy to the real case established by Matusita (1955) we introduce the concept of affinity between two complex distribution functions. We also establish a concrete expression for the affinity between two complex k-variate normal distributions when the covariance matrices assume a special form. Generalizations of these results are presented and the expressions here obtained are compared with those obtained by Matusita (1966, 1967) relative to the affinity between real k-variate normal distributions....

An exploratory canonical analysis approach for multinomial populations based on the φ -divergence measure

Julio A. Pardo, Leandro Pardo, María Del Carmen Pardo, K. Zografos (2004)


In this paper we consider an exploratory canonical analysis approach for multinomial population based on the φ -divergence measure. We define the restricted minimum φ -divergence estimator, which is seen to be a generalization of the restricted maximum likelihood estimator. This estimator is then used in φ -divergence goodness-of-fit statistics which is the basis of two new families of statistics for solving the problem of selecting the number of significant correlations as well as the appropriateness...

An interpolation problem for multivariate stationary sequences

Lutz Klotz (2000)


Let 𝐗 and 𝐘 be stationarily cross-correlated multivariate stationary sequences. Assume that all values of 𝐘 and all but one values of 𝐗 are known. We determine the best linear interpolation of the unknown value on the basis of the known values and derive a formula for the interpolation error matrix. Our assertions generalize a result of Budinský [1].

Aplicaciones de los teoremas de separación para valores singulares de matrices al análisis de la redundancia.

Francisco Carmona (1988)


El análisis de la redundancia constituye una alternativa al análisis de la correlación canónica en el estudio de la relación entre dos grupos de variables.La utilización de normas invariantes por matrices unitarias permite generalizar la definición de índice de la redundancia. Con los teoremas de separación para valores singulares de matrices se obtienen caracterizaciones similares del análisis de la redundancia y del análisis de la correlación canónica.En el problema de la regresión reduciendo...

Application of the Rasch model in categorical pedigree analysis using MCEM: I binary data

G. Qian, R. M. Huggins, D. Z. Loesch (2004)

Discussiones Mathematicae Probability and Statistics

An extension of the Rasch model with correlated latent variables is proposed to model correlated binary data within families. The latent variables have the classical correlation structure of Fisher (1918) and the model parameters thus have genetic interpretations. The proposed model is fitted to data using a hybrid of the Metropolis-Hastings algorithm and the MCEM modification of the EM-algorithm and is illustrated using genotype-phenotype data on a psychological subtest in families where some members...

Asymmetric semilinear copulas

Bernard De Baets, Hans De Meyer, Radko Mesiar (2007)


We complement the recently introduced classes of lower and upper semilinear copulas by two new classes, called vertical and horizontal semilinear copulas, and characterize the corresponding class of diagonals. The new copulas are in essence asymmetric, with maximum asymmetry given by 1 / 16 . The only symmetric members turn out to be also lower and upper semilinear copulas, namely convex sums of Π and M .

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