کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
9492839 1333836 2005 7 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Spherical distributions: Schoenberg (1938) revisited
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Spherical distributions: Schoenberg (1938) revisited
چکیده انگلیسی
An m-dimensional random vector X is said to have a spherical distribution if and only if its characteristic function is of the form φ(∥t∥), where t∈Rm, ∥.∥ denotes the usual Euclidean norm, and φ is a characteristic function on R. A more intuitive description is that the probability density function of X is constant on spheres. The class Φm of these characteristic functions φ is fundamental in the theory of spherical distributions on Rm. An important result, which was originally proved by Schoenberg (Ann. Math. 39(4) (1938) 811-841), is that the underlying characteristic function φ of a spherically distributed random m-vector X belongs to Φ∞ if and only if the distribution of X is a scale mixture of normal distributions. A proof in the context of exchangeability has been given by Kingman (Biometrika 59 (1972) 492-494). Using probabilistic tools, we will give an alternative proof in the spirit of Schoenberg we think is more elegant and less complicated.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Expositiones Mathematicae - Volume 23, Issue 3, 15 September 2005, Pages 281-287
نویسندگان
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