Abstract

The well-known inspection paradox of renewal theory states that, in expectation, the inspection interval is larger than a common renewal interval, in general. For a random inspection time, which includes the deterministic case, and a delayed renewal process, representations of the expected length of an inspection interval and related inequalities in terms of covariances are shown. Datasets of eruption times of Beehive Geyser and Riverside Geyser in Yellowstone National Park, as well as several distributional examples, illustrate the findings.

中文翻译：

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用随机时间量化检查悖论

摘要

众所周知的更新理论检查悖论指出，在预期中，检查间隔通常大于常见的更新间隔。对于随机检查时间（包括确定性情况和延迟更新过程），显示了检查间隔的预期长度和协方差方面的相关不等式的表示。黄石国家公园蜂巢间歇泉和河滨间歇泉喷发时间的数据集以及几个分布示例说明了这些发现。