On variability of the mean inactivity time at random time

Bin Lu ()
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Bin Lu: Lanzhou Jiaotong University

Statistical Papers, 2025, vol. 66, issue 4, No 21, 16 pages

Abstract: Abstract In this paper, we explore the mean inactivity time (MIT) with respect to an item at a random time. We demonstrate that the MIT at random times closely aligns with established measures of variability. Our findings include a decomposition result, which shows that the MIT, like other variability measures, can be represented using covariance. Additionally, under the proportional reversed hazard rates (PRH) model, we show that the MIT, depending on the proportionality parameter, includes Gini’s mean difference and cumulative Tsallis entropy as specific cases. And the empirical cumulative Tsallis entropy is also proposed to estimate the $$E(X_{(T)})$$ E ( X ( T ) ) .

Keywords: Mean inactivity time; Variability measures; Proportional reversed hazards (PRH) model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00362-025-01719-5

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