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Hyperbolic cosine ratio and hyperbolic sine ratio random fields

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  • Ma, Chunsheng

Abstract

This paper introduces several vector random fields whose finite-dimensional characteristic functions are of hyperbolic type, including generalized logistic, hyperbolic secant, hyperbolic tangent, hyperbolic cosine ratio, and hyperbolic sine ratio vector random fields. They are elliptically contoured vector random fields with all orders of moments, and are infinitely divisible. In the scalar case, we make the peakedness comparison among these random fields. Hyperbolic cosine ratio and hyperbolic since ratio Lévy processes are formulated as well.

Suggested Citation

  • Ma, Chunsheng, 2021. "Hyperbolic cosine ratio and hyperbolic sine ratio random fields," Statistics & Probability Letters, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:stapro:v:179:y:2021:i:c:s0167715221001747
    DOI: 10.1016/j.spl.2021.109212
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    References listed on IDEAS

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    1. Devroye, Luc, 2009. "On exact simulation algorithms for some distributions related to Jacobi theta functions," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2251-2259, November.
    2. Huang, Steel T. & Cambanis, Stamatis, 1979. "Spherically invariant processes: Their nonlinear structure, discrimination, and estimation," Journal of Multivariate Analysis, Elsevier, vol. 9(1), pages 59-83, March.
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