论文标题
联合离散和连续矩阵分布建模
Joint discrete and continuous matrix distribution modelling
论文作者
论文摘要
在本文中，我们在$ \ mathbb {r} _ {+} \ times \ mathbb {n} $上引入了双变量分布，这是由单个基础马尔可夫跳跃过程引起的。边缘分布分别是相类型和离散的相型分布，它们允许用于建模的灵活行为。我们表明，分布在$ \ mathbb {r} _ {+} \ times \ mathbb {n} $上的分布类中是密集的，并得出了其一些主要属性，所有这些属性都是根据矩阵计算的。此外，我们为分布参数的统计估计开发了有效的EM算法。在本文的最后一部分中，我们将方法应用于保险数据集，在该数据集中，我们对索赔的数量和保单持有人的平均索赔规模进行了建模，这被认为是有利的。后者分析的另一个结果是，整个投资组合中的总损耗大小比独立相型模型要好得多。
In this paper we introduce a bivariate distribution on $\mathbb{R}_{+} \times \mathbb{N}$ arising from a single underlying Markov jump process. The marginal distributions are phase-type and discrete phase-type distributed, respectively, which allow for flexible behavior for modeling purposes. We show that the distribution is dense in the class of distributions on $\mathbb{R}_{+} \times \mathbb{N}$ and derive some of its main properties, all explicit in terms of matrix calculus. Furthermore, we develop an effective EM algorithm for the statistical estimation of the distribution parameters. In the last part of the paper, we apply our methodology to an insurance dataset, where we model the number of claims and the mean claim sizes of policyholders, which is seen to perform favorably. An additional consequence of the latter analysis is that the total loss size in the entire portfolio is captured substantially better than with independent phase-type models.
