Asymptotics for the maxima and minima of Hüsler-Reiss bivariate Gaussian arrays

Liao, Xiaofeng; Peng, Zuoxiang

doi:10.1007/s10687-014-0196-7

Cited by 15 publications

(5 citation statements)

References 21 publications

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“…For bivariate Gaussian arrays under relaxation assumptions, see [19]. For dissimilar improved assumptions, see [20] and [21]. Let m n = min{X i , 1 ≤ i ≤ n} denote the partial minimum of {X i , i ≥ 1}.…”

Section: Introductionmentioning

confidence: 99%

Expansions of maximum and minimum from Generalized Maxwell distribution

Huang

2020

Preprint

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Generalized Maxwell distribution is an extension of the classic Maxwell distribution. In this paper, we concentrate on the joint distributional asymptotics of normalized maxima and minima. Under optimal normalizing constants, asymptotic expansions of joint distribution and density for normalized partial maxima and minima are established. These expansions are used to educe speeds of convergence of joint distribution and density of normalized maxima and minima tending to its corresponding ultimate limits. Numerical analysis are provided to support our results.

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Section: Introductionmentioning

confidence: 99%

Expansions of maximum and minimum from Generalized Maxwell distribution

Huang

2020

Preprint

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“…Davis (1979) established the joint limiting distribution of maxima and minima of weakly dependent stationary sequences, and weakly dependent stationary Gaussian processes was studied by Berman (1971). For the asymptotic distributions of maxima and minima on bivariate Hüsler-Reiss models, see Liao and Peng (2015) and Lu and Peng (2017).…”

Section: Introductionmentioning

confidence: 99%

Maxima and minima of homogeneous Gaussian random fields over continuous time and uniform grids

Peng

2019

Stochastics

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In this paper, for centered homogeneous Gaussian random fields the joint limiting distributions of normalized maxima and minima over continuous time and uniform grids are investigated. It is shown that maxima and minima are asymptotic dependent for strongly dependent homogeneous Gaussian random field with the choice of sparse grid, Pickands' grid or dense grid, while for the weakly dependent Gaussian random field maxima and minima are asymptotically independent.

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“…Realistic models can be obtained by deriving expansions for the joint distribution of the minimum and maximum. Liao and Peng (2015) and Lu and Peng (2017) give the most recent work on the asymptotics of the joint distribution of the minimum and maximum.…”

Section: Introductionmentioning

confidence: 99%