论文标题
带有一些新颖应用的离散循环分布的家族
Families of discrete circular distributions with some novel applications
论文作者
论文摘要
由一些尖端循环数据的动机，例如来自智能家居技术和在线和赌场的轮盘旋转，我们在圆圈上构建了一些新的丰富的离散分布类别。我们提供了四种新的一般构造方法，即（i）最大熵，（ii）中心包裹，（iii）边缘化和（iv）条件化方法。我们激励这些方法在线上，然后在循环案例上进行工作，并提供一些属性，以深入了解这些结构。我们主要关注循环位置家庭的最后两种方法（iii）和（iv），因为它们适合一般方法。我们表明，边缘化和有条理的离散循环位置家庭从其父母连续家庭那里继承了重要的特性。特别是，对于冯·米塞斯（Von Mises）并将凯奇（Cauchy）作为母体分布包裹，我们检查了它们的特性，包括最大似然估计量，假设均匀性测试并进行了序列独立性的测试。使用我们的离散圆形分布，我们演示了如何确定数据何时以序列出现以及如何拟合该分布的混合物。给出了触发工作的说明性示例。例如，对于轮盘数据，我们测试了均匀性（无偏），测试串行相关性，检测流盘旋转旋转速体数据中的变更点以及拟合混合物。我们使用混合物分析智能家庭数据。我们研究了忽略潜在人口的离散性的效果，并讨论边缘化的方法与有条件的方法。我们将各种偏斜和峰度的家庭提供给不规则晶格的支持的家庭，并通过在圆环上显示构造来讨论一般歧管的潜在扩展。
Motivated by some cutting edge circular data such as from Smart Home technologies and roulette spins from online and casino, we construct some new rich classes of discrete distributions on the circle. We give four new general methods of construction, namely (i) maximum entropy, (ii) centered wrapping, (iii) marginalized and (iv) conditionalized methods. We motivate these methods on the line and then work on the circular case and provide some properties to gain insight into these constructions. We mainly focus on the last two methods (iii) and (iv) in the context of circular location families, as they are amenable to general methodology. We show that the marginalized and conditionalized discrete circular location families inherit important properties from their parent continuous families. In particular, for the von Mises and wrapped Cauchy as the parent distribution, we examine their properties including the maximum likelihood estimators, the hypothesis test for uniformity and give a test of serial independence. Using our discrete circular distributions, we demonstrate how to determine changepoint when the data arise in a sequence and how to fit mixtures of this distribution. Illustrative examples are given which triggered the work. For example, for roulette data, we test for uniformity (unbiasedness) , test for serial correlation, detect changepoint in streaming roulette-spins data, and fit mixtures. We analyse a smart home data using our mixtures. We examine the effect of ignoring discreteness of the underlying population, and discuss marginalized versus conditionalized approaches. We give various extensions of the families with skewness and kurtosis, to those supported on an irregular lattice, and discuss potential extension to general manifolds by showing a construction on the torus
