The theory of concentrated Langevin distributions
The theory of concentrated Langevin distributions
复制标题
集中朗之万分布理论
DOI：
10.1016/0047-259x(84)90047-2
复制
发表时间：
1984
影响因子：
1.6
通讯作者：
G. Watson
中科院分区：
文献类型：
--
作者：
G. Watson
朗之万（或费舍尔-冯·米塞斯）分布的密度与exp κμ′ x成比例，其中x和模态向量μ是R q中的单位向量。κ（≥ 0）称为浓度参数。当浓度参数趋于无穷大时，检验关于m分布的模态向量的假设的统计量的分布大大简化。当k 1，.，k m已知但趋于无穷大，以及k 1，.，k m未知但等于趋于无穷大的k时，得到了适合统计量的非零分布。这三个原假设是H 01：μ= μ 0（m= 1），H 02：μ 1=.= μ m，H 03：μ i = V，i= 1，.，m。在每种情况下，都采取一系列倾向于原假设的备选方案。
The density of the Langevin (or Fisher-Von Mises) distribution is proportional to exp κμ′ x, where x and the modal vector μ are unit vectors in R q. κ (≥ 0) is called the concentration parameter. The distribution of statistics for testing hypotheses about the modal vectors of m distributions simplify greatly as the concentration parameters tend to infinity. The non-null distributions are obtained for statistics appropriate when κ 1,…, κ m are known but tend to infinity, and are unknown but equal to κ which tends to infinity. The three null hypotheses are H 01: μ= μ 0 (m= 1), H 02: μ 1=…= μ m, H 03: μ i ϵ V, i= 1,…, m In each case a sequence of alternatives is taken tending to the null hypothesis.