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Beyond the Gaussian Models

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Random Fields for Spatial Data Modeling

Part of the book series: Advances in Geographic Information Science ((AGIS))

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Abstract

This chapter focuses on the modeling of non-Gaussian probability distributions. The main reason for discussing non-Gaussian models is the fact that spatial data often exhibit properties such as (i) strictly positive values (ii) asymmetric (skewed) probability distributions (iii) long positive tails (e.g., power-law decay of the pdf) and (iv) compact support.

\(M\alpha \nu \theta \acute {\alpha }\nu \omega \nu \) \(K\acute {\alpha }\mu \nu \varepsilon \) Do not get tired of learning

Delphic maxim

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Notes

  1. 1.

    Note that the role of X(ω) and Y(ω) is reversed herein with respect to the expression of Jacobi’s theorem in the Appendix A, since the pdf of Y(ω) is assumed to be known.

  2. 2.

    The parameter h of TGH random fields should not be confused with the normalized distance h.

  3. 3.

    There are slight notational variations across different fields; for example, in physics the Gaussian exponent is y 2 instead of y 2∕2, and in geostatistics the sign (−1)m is often dropped. Such differences lead to respective variations in the relations that involve the Hermite polynomials.

  4. 4.

    Available online at: https://papers.nips.cc/

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Hristopulos, D.T. (2020). Beyond the Gaussian Models. In: Random Fields for Spatial Data Modeling. Advances in Geographic Information Science. Springer, Dordrecht. https://doi.org/10.1007/978-94-024-1918-4_14

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