Hyperbolic cosine ratio and hyperbolic sine ratio random fields

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.