2017/09/30 by S. Rao Jammalamadaka, Jammalamadaka, S. Rao, György Terdik +1 · 1 citation
Computer Science · Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #62H11 #62H15 #Bayesian Methods and Mixture Models #FOS: Computer and information sciences #Geochemistry and Geologic Mapping #Geophysical and Geoelectrical Methods #Methodology (stat.ME) #Scientific Research and Discoveries #Statistical and numerical algorithms
paper · pdf · doi:10.48550/arxiv.1710.00253
openalex publication_date 2017/09/30 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
Fourier analysis and representation of circular distributions in terms of\ntheir Fourier coefficients, is quite commonly discussed and used for model-free\ninference such as testing uniformity and symmetry etc. in dealing with\n2-dimensional directions. However a similar discussion for spherical\ndistributions, which are used to model 3-dimensional directional data, has not\nbeen fully developed in the literature in terms of their harmonics. This paper,\nin what we believe is the first such attempt, looks at the probability\ndistributions on a unit sphere, through the perspective of spherical harmonics,\nanalogous to the Fourier analysis for distributions on a unit circle. Harmonic\nrepresentations of many currently used spherical models are presented and\ndiscussed. A very general family of spherical distributions is then introduced,\nspecial cases of which yield many known spherical models. Through the prism of\nharmonic analysis, one can look at the mean direction, dispersion, and various\nforms of symmetry for these models in a generic setting. Aspects of\ndistribution free inference such as estimation and large-sample tests for these\nsymmetries, are provided. The paper concludes with a real-data example\nanalyzing the longitudinal sunspot activity.\n