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- W2963972005 abstract "This paper concerns space-sphere point processes, that is, point processes on the product space of $mathbb {R}^{d}$ (the d-dimensional Euclidean space) and $mathbb {S}^{k}$ (the k-dimensional sphere). We consider specific classes of models for space-sphere point processes, which are adaptations of existing models for either spherical or spatial point processes. For model checking or fitting, we present the space-sphere K-function which is a natural extension of the inhomogeneous K-function for point processes on $mathbb {R}^{d}$ to the case of space-sphere point processes. Under the assumption that the intensity and pair correlation function both have a certain separable structure, the space-sphere K-function is shown to be proportional to the product of the inhomogeneous spatial and spherical K-functions. For the presented space-sphere point process models, we discuss cases where such a separable structure can be obtained. The usefulness of the space-sphere K-function is illustrated for real and simulated datasets with varying dimensions d and k." @default.
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- W2963972005 date "2019-04-12" @default.
- W2963972005 modified "2023-10-09" @default.
- W2963972005 title "Structured Space-Sphere Point Processes and K-Functions" @default.
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- W2963972005 doi "https://doi.org/10.1007/s11009-019-09712-w" @default.
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