Bivariate distributions with Gaussian-type dependence structure

Shaul K. Bar-Lev; Abram M. Kagan

doi:10.1080/03610910902936158

Bivariate distributions with Gaussian-type dependence structure

Shaul K. Bar-Lev, Abram M. Kagan

Department of Statistics

Research output: Contribution to journal › Article › peer-review

Abstract

Let Zi=(Xi, Yi), i=1, n be independent random vectors with E|Z _i|2. We describe in terms of characteristic functions the distributions of Z_i with the following property: all pairs of uncorrelated linear forms L₁=a₁X₁++a _nX_n and L₂=b₁Y₁++b _nY_n depending on the first and second components of Z ₁, Z_n, respectively, are independent. Although the above property formally concerns the dependence structure of the first and second components only, it imposes strict restrictions on the marginal distributions.

Original language	English
Pages (from-to)	2669-2676
Number of pages	8
Journal	Communications in Statistics - Theory and Methods
Volume	38
Issue number	16-17
DOIs	https://doi.org/10.1080/03610910902936158
State	Published - Jan 2009

Keywords

Dependence
Linear forms
Vershik's theorem

ASJC Scopus subject areas

Statistics and Probability

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10.1080/03610910902936158

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N2 - Let Zi=(Xi, Yi), i=1, n be independent random vectors with E|Z i|2. We describe in terms of characteristic functions the distributions of Zi with the following property: all pairs of uncorrelated linear forms L1=a1X1++a nXn and L2=b1Y1++b nYn depending on the first and second components of Z 1, Zn, respectively, are independent. Although the above property formally concerns the dependence structure of the first and second components only, it imposes strict restrictions on the marginal distributions.

AB - Let Zi=(Xi, Yi), i=1, n be independent random vectors with E|Z i|2. We describe in terms of characteristic functions the distributions of Zi with the following property: all pairs of uncorrelated linear forms L1=a1X1++a nXn and L2=b1Y1++b nYn depending on the first and second components of Z 1, Zn, respectively, are independent. Although the above property formally concerns the dependence structure of the first and second components only, it imposes strict restrictions on the marginal distributions.

KW - Dependence

KW - Linear forms

KW - Vershik's theorem

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JO - Communications in Statistics - Theory and Methods

JF - Communications in Statistics - Theory and Methods

IS - 16-17

ER -

Bivariate distributions with Gaussian-type dependence structure

Abstract

Keywords

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