APPROXIMATE INDEPENDENCE OF DISTRIBUTIONS ON SPHERES AND THEIR STABILITY PROPERTIES

• 成果类型: Article
• 署名作者: RACHEV, ST; RUSCHENDORF, L
• 署名单位: University of Munster
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176990346
• 发表日期: 1991
• 页码: 1311-1337
• 关键词: Extreme value theory; CONVERGENCE; rates

摘要

Let zeta be chosen at random on the surface of the p-sphere in R(n), Op,n : = {x is-an-element-of R(n): SIGMA-i = 1n \x(i)\p = n}. If p = 2, then the first k components zeta-1,...,zeta-k are, for k fixed, in the limit as n --> infinity independent standard normal. Considering the general case p > 0, the same phenomenon appears with a distribution F(p) in an exponential class E. F(p) can be characterized by the distribution of quotients of sums, by conditional distributions and by a maximum entropy condition. These characterizations have some interesting stability properties. Some discrete versions of this problem and some applications to de Finetti-type theorems are discussed.