On variability of the mean remaining lifetime at random age

Majid Asadi () and Maxim Finkelstein ()
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Majid Asadi: University of Isfahan
Maxim Finkelstein: University of the Free State

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2024, vol. 33, issue 3, No 8, 717-730

Abstract: Abstract In this short communication, we discuss the remaining lifetime and the mean remaining lifetime (MRL) of an item with a random age. We show that the MRL at random age is closely related to some well-known variability measures. First, we provide a decomposition result showing that the MRL at random age, similar to other variability measures, has a covariance representation. Under the proportional hazards (PH) model, we show that the MRL, depending on the parameter of proportionality, subsumes the Gini’s mean difference and the cumulative residual entropy as special cases. It is also shown that, under the PH model, the MRL can be expressed via the equilibrium distribution and the mean number of events in the generalized Pólya process.

Keywords: Random age; Variability measures; Proportional hazards; Reliability function; Mean remaining lifetime; Primary: 62N05; Secondary: 62E10 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s11749-023-00917-3

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