Matrix generalized elliptical binomial series under real normed division algebras and the central matrix variate beta distribution
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866912060223258624 |
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| author | Caro-Lopera, Francisco J. Díaz-García, José A. |
| author_facet | Caro-Lopera, Francisco J. Díaz-García, José A. |
| contents | In this paper we provide a matrix extension of the scalar binomial series under elliptical contoured models and real normed division algebras. The classical hypergeometric series ${}_{1}F_{0}^β(a;\mathbf{Z})={}_{1}^{k}P_{0}^{β,1}(1:a;\mathbf{Z})=|\mathbf{I}-\mathbf{Z}|^{-a}$ of Jack polynomials are now seen as an invariant generalized determinant with a series representation indexed by any elliptical generator function. In particular, a corollary emerges for a simple derivation of the central matrix variate beta type II distribution under elliptically contoured models in the unified real, complex, quaternions and octonions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_04023 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Matrix generalized elliptical binomial series under real normed division algebras and the central matrix variate beta distribution Caro-Lopera, Francisco J. Díaz-García, José A. Statistics Theory In this paper we provide a matrix extension of the scalar binomial series under elliptical contoured models and real normed division algebras. The classical hypergeometric series ${}_{1}F_{0}^β(a;\mathbf{Z})={}_{1}^{k}P_{0}^{β,1}(1:a;\mathbf{Z})=|\mathbf{I}-\mathbf{Z}|^{-a}$ of Jack polynomials are now seen as an invariant generalized determinant with a series representation indexed by any elliptical generator function. In particular, a corollary emerges for a simple derivation of the central matrix variate beta type II distribution under elliptically contoured models in the unified real, complex, quaternions and octonions. |
| title | Matrix generalized elliptical binomial series under real normed division algebras and the central matrix variate beta distribution |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2410.04023 |