## Abstract

First, we consider items that are incepted into operation having already a random (initial) age and define the corresponding remaining lifetime. We show that these random variables are identically distributed when the age distribution is equal to the equilibrium distribution of the renewal theory. Then we consider real populations of items that were incepted into operation (were born) at different instants of time and obtain some useful inequalities between the population age and the remaining lifetime using reasoning similar to that employed in population studies. We also discuss the aging properties of populations using different stochastic orders.

Original language | English |
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Pages (from-to) | 199-213 |

Number of pages | 15 |

Journal | Statistical Papers |

Volume | 59 |

Issue number | 1 |

DOIs | |

State | Published - 1 Mar 2018 |

### Bibliographical note

Publisher Copyright:© 2016, Springer-Verlag Berlin Heidelberg.

## Keywords

- Equilibrium distribution
- Random initial age
- Stable population
- Stationary population
- Stochastic ordering