论文标题
将不均匀的相型分布拟合到数据：单变量和多变量情况
Fitting inhomogeneous phase-type distributions to data: the univariate and the multivariate case
论文作者
论文摘要
最近在Albrecher和Bladt（2019）中引入了不均匀的相位类型分布（IPH）的类别，作为经典相相（PH）分布的扩展。像pH分布一样，iPH类在正线的分布类别中也很稠密，但是在较重的尾巴存在下会导致更多的模型。在本文中，我们为此类提出了一个合适的程序，以给出数据。此外，我们考虑了Kulkarni的多元相型类（Kulkarni，1989）的类似扩展，以与所产生的新且灵活的多元分布类别的不均匀框架和研究参数估计。作为副产品，我们修改了先前建议的均匀多变量相型情况的拟合程序，并为审查数据提供了适当的适应性。在几个数值示例中说明了该算法的性能，包括模拟保险数据和现实保险数据。
The class of inhomogeneous phase-type distributions (IPH) was recently introduced in Albrecher and Bladt (2019) as an extension of the classical phase-type (PH) distributions. Like PH distributions, the class of IPH is dense in the class of distributions on the positive halfline, but leads to more parsimonious models in the presence of heavy tails. In this paper we propose a fitting procedure for this class to given data. We furthermore consider an analogous extension of Kulkarni's multivariate phase-type class (Kulkarni, 1989) to the inhomogeneous framework and study parameter estimation for the resulting new and flexible class of multivariate distributions. As a by-product, we amend a previously suggested fitting procedure for the homogeneous multivariate phase-type case and provide appropriate adaptations for censored data. The performance of the algorithms is illustrated in several numerical examples, both for simulated and real-life insurance data.
