Numerical simulation for the climatic statistical structure with the new correlation functions of the extended polynomial form and the extended exponential form

Onn, Shing-Chung; Wang, Kuang-Horng; Tseng, Chung-Yi

doi:10.1016/0273-1177(94)90119-8

Cited by 2 publications

(2 citation statements)

References 11 publications

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“…Then we turn to isotropic covariance functions of locally polynomial type, C(h) = n k=0 a k |h| k for h ∈ R d , |h| ≤ 1. Covariance models of this form have been fitted frequently; see Mitchell et al (1990), Currin et al (1991), Wiencek and Stoyan (1993), Onn et al (1994), and the references in Gneiting (1999a). Section 4.3 discusses the quadratic case, and Section 4.4 characterizes locally cubic covariances.…”

Section: Examples and Applicationsmentioning

confidence: 99%

Analogies and correspondences between variograms and covariance functions

Gneiting

Sasvári

Schlather

2001

Advances in Applied Probability

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Variograms and covariance functions are key tools in geostatistics. However, various properties, characterizations, and decomposition theorems have been established for covariance functions only. We present analogous results for variograms and explore the connections with covariance functions. Our findings include criteria for covariance functions on intervals, and we apply them to exponential models, fractional Brownian motion, and locally polynomial covariances. In particular, we characterize isotropic locally polynomial covariance functions of degree 3.

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Section: Examples and Applicationsmentioning

confidence: 99%

Analogies and correspondences between variograms and covariance functions

Gneiting

Sasvári

Schlather

2001

Advances in Applied Probability

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“…Many authors have fitted isotropic correlation models of the polynomial type, c(x) = 1 + n k=1 a k x k , to observed correlations on bounded domains. Stol (1981, p. 46) provides a selection of references for n up to 3, and Wiencek and Stoyan (1993) and Onn et al (1994) have recently employed models of degree n = 4 and higher. Since the monomials t k , k ≥ 0, are eigenfunctions of the turning bands operator (Matheron 1973), the same approach works for higher order models, and the problem reduces to the onedimensional case.…”

Section: Commentsmentioning

confidence: 99%

Isotropic correlation functions ond-dimensional balls

Gneiting

1999

Advances in Applied Probability

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A popular procedure in spatial data analysis is to fit a line segment of the form c(x) = 1 - α ||x||, ||x|| < 1, to observed correlations at (appropriately scaled) spatial lag x in d-dimensional space. We show that such an approach is permissible if and only if the upper bound depending on the spatial dimension d. The proof relies on Matheron's turning bands operator and an extension theorem for positive definite functions due to Rudin. Side results and examples include a general discussion of isotropic correlation functions defined on d-dimensional balls.

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Numerical simulation for the climatic statistical structure with the new correlation functions of the extended polynomial form and the extended exponential form

Cited by 2 publications

References 11 publications

Analogies and correspondences between variograms and covariance functions

Analogies and correspondences between variograms and covariance functions

Isotropic correlation functions ond-dimensional balls

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