论文标题
基于熵的拟合测试，用于广义von mises-fisher分布及其他
The entropy based goodness of fit tests for generalized von Mises-Fisher distributions and beyond
论文作者
论文摘要
我们介绍了一些新的单峰旋转不变方向分布，这些分布将概括为von mises-fisher分布。我们提出了三种类型的分布，其中一种代表轴向数据。对于每种新类型，我们通过矩和最大似然的方法提供公式和参数估计器的简短计算研究。本文的主要目的是开发拟合测试的优点，以检测样品条目遵循基于最大熵原理的涉及广义的von mises分布之一。我们使用$ k $ th最近的邻居距离估计器，并证明其$ l^2 $ - 一致性。我们检查了测试统计数据的行为，在模拟样本上找到临界值并计算测试的功率。我们将拟合测试的优点应用于玻璃纤维增强复合材料的局部纤维方向，并检测遵循轴向广义von mises的样品 - 捕虫分布。
We introduce some new classes of unimodal rotational invariant directional distributions, which generalize von Mises-Fisher distribution. We propose three types of distributions, one of which represents axial data. For each new type we provide formulae and short computational study of parameter estimators by the method of moments and the method of maximum likelihood. The main goal of the paper is to develop the goodness of fit test to detect that sample entries follow one of the introduced generalized von Mises--Fisher distribution based on the maximum entropy principle. We use $k$th nearest neighbour distances estimator of Shannon entropy and prove its $L^2$-consistency. We examine the behaviour of the test statistics, find critical values and compute power of the test on simulated samples. We apply the goodness of fit test to local fiber directions in a glass fibre reinforced composite material and detect the samples which follow axial generalized von Mises--Fisher distribution.
