Abstract
Many important classes of multivariate distributions arising from reliability modeling are the distributions of correlated first passage times of certain multivariate point processes. In this paper, we obtain results that compare variability and dependence structure of these correlated first passage times, in the sense of directionally convex ordering. Under certain conditions, we also obtain some easily computable distributional bounds for the first passage times whose joint distributions can not be expressed explicitly.
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Li, H., Xu, S.H. Directionally Convex Comparison of Correlated First Passage Times. Methodology and Computing in Applied Probability 3, 365–378 (2001). https://doi.org/10.1023/A:1015412103008
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DOI: https://doi.org/10.1023/A:1015412103008