区间剔除的非均质交替更新过程模型

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
M. N. M. van Lieshout, R. L. Markwitz
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引用次数: 0

摘要

以往的区间删失数据建模方法通常依赖于同质性假设,即假设删失机制、发生时间的基本分布或两者都是时间不变的。在这项工作中,我们引入了一个模型,允许在这两种情况下的非均质性行为。特别是,我们概述了一种基于非均质交替更新过程的删减机制,其中假设区间的生成与时间有关,我们还为基本的发生时间分布提出了一个马尔可夫点过程模型。我们证明了这一过程的存在性,并推导出了给定区间的发生时间的条件分布。我们提供了一个框架,在此框架内可以对该过程进行精确建模,随后通过一些示例将我们的模型与同质方法进行比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A non-homogeneous alternating renewal process model for interval censoring

Previous approaches to modelling interval-censored data have often relied on assumptions of homogeneity in the sense that the censoring mechanism, the underlying distribution of occurrence times, or both, are assumed to be time-invariant. In this work, we introduce a model which allows for non-homogeneous behaviour in both cases. In particular, we outline a censoring mechanism based on a non-homogeneous alternating renewal process in which interval generation is assumed to be time-dependent, and we propose a Markov point process model for the underlying occurrence time distribution. We prove the existence of this process and derive the conditional distribution of the occurrence times given the intervals. We provide a framework within which the process can be accurately modelled, and subsequently compare our model to the homogeneous approach through a number of illustrative examples.

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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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