论文标题
分析半马尔可夫模型的寄居时间分布
Analysis of sojourn time distributions for semi-Markov models
论文作者
论文摘要
该报告旨在表征某些自然来自半马尔科夫模型的居民时间分布。为此，它描述了一个离散分布的家族，该家族扩展了有限和无限时间的几何分布。我们显示了目前生成函数以及均值和方差的公式，并给出具体的示例。我们考虑特定的参数化亚家族；线性因子模型和简单的多项式因子模型。我们从这些分布中模拟图形，并为每个亚家族的参数（包括非常小的样本量）的最大似然估计器（MLE）求解。然后，该报告描述了MLE的偏差和方差的确定，并显示了它们与Fisher信息的关系，它们随着样本量的增加而表现出适当的浓度效应。最后，该报告解决了这些方法在实验数据中的应用，这表明与简单多项式因子模型非常吻合。
This report aims to characterise certain sojourn time distributions that naturally arise from semi-Markov models. To this end, it describes a family of discrete distributions that extend the geometric distribution for both finite and infinite time. We show formulae for the moment generating functions and the mean and variance, and give specific examples. We consider specific parametrised subfamilies; the linear factor model and simple polynomial factor models. We numerically simulate drawing from these distributions and solving for the Maximum Likelihood Estimators (MLEs) for the parameters of each subfamily, including for very small sample sizes. The report then describes the determination of the bias and variance of the MLEs, and shows how they relate to the Fisher information, where they exhibit appropriate concentration effects as the sample size increases. Finally, the report addresses an application of these methods to experimental data, which shows a strong fit with the simple polynomial factor model.
