### Abstract

The life table population identity was first discovered by Nicolas Brouard in the mid-1980s but brought into the mainstream demographic literature when rediscovered by James Carey in the early 2000s in the context of fruit fly demography. Based on the assumption of stationarity, the identity states that the fraction age x in a population equals the fraction with x years to live. The purpose of this chapter is to describe the contexts within which both Brouard and Carey discovered the identity, present a proof, three extensions, and two applications, the latter of which involves estimation of mean age and age structure in wild fruit fly populations. At the end we discuss the relevance of the identity to demography in general and to human demography in particular.

Original language | English (US) |
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Title of host publication | Handbook of Statistics |

Editors | Arni S.R. Srinivasa Rao, C.R. Rao |

Publisher | Elsevier B.V. |

Pages | 155-186 |

Number of pages | 32 |

ISBN (Print) | 9780444640727 |

DOIs | |

Publication status | Published - Jan 1 2018 |

### Publication series

Name | Handbook of Statistics |
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Volume | 39 |

ISSN (Print) | 0169-7161 |

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### Keywords

- Age-structure theorems
- Brouard's Theorem
- Carey's Equality
- Life table populations
- Nonstationary populations
- Stationary populations

### ASJC Scopus subject areas

- Statistics and Probability
- Modeling and Simulation
- Applied Mathematics

### Cite this

*Handbook of Statistics*(pp. 155-186). (Handbook of Statistics; Vol. 39). Elsevier B.V.. https://doi.org/10.1016/bs.host.2018.08.002