On variability of the mean remaining lifetime at random age

• Majid Asadi ^[1] ; Maxim Finkelstein ^[2]
  1. [1] University of Isfahan

     University of Isfahan

     Irán

     
  2. [2] University of the Free State

     University of the Free State

     Mangaung, Sudáfrica

     
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 33, Nº. 3, 2024, págs. 717-730
• Idioma: inglés
• DOI: 10.1007/s11749-023-00917-3
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.