Report
Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials
| العنوان: | Multivariate Jacobi and Laguerre polynomials, infinite-dimensional extensions, and their probabilistic connections with multivariate Hahn and Meixner polynomials |
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| المؤلفون: | Griffiths, Robert C., Spanó, Dario |
| المصدر: | Bernoulli 2011, Vol. 17, No. 3, 1095-1125 |
| سنة النشر: | 2008 |
| المجموعة: | Mathematics Statistics |
| مصطلحات موضوعية: | Mathematics - Probability, Mathematics - Statistics Theory |
| الوصف: | Multivariate versions of classical orthogonal polynomials such as Jacobi, Hahn, Laguerre and Meixner are reviewed and their connection explored by adopting a probabilistic approach. Hahn and Meixner polynomials are interpreted as posterior mixtures of Jacobi and Laguerre polynomials, respectively. By using known properties of gamma point processes and related transformations, a new infinite-dimensional version of Jacobi polynomials is constructed with respect to the size-biased version of the Poisson--Dirichlet weight measure and to the law of the gamma point process from which it is derived. Comment: Published in at http://dx.doi.org/10.3150/10-BEJ305 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm) |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.3150/10-BEJ305 |
| URL الوصول: | http://arxiv.org/abs/0809.1431 |
| رقم الانضمام: | edsarx.0809.1431 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.3150/10-BEJ305 |
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