Background
Type: Article

On variability of the mean remaining lifetime at random age

Journal: Test (11330686)Year: September 2024Volume: 33Issue: Pages: 717 - 730
Asadi M.a Finkelstein M.
DOI:10.1007/s11749-023-00917-3Language: English

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. © The Author(s) under exclusive licence to Sociedad de Estadística e Investigación Operativa 2024.