### 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) |
---|---|

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 | |

State | Published - Jan 1 2018 |

### Publication series

Name | Handbook of Statistics |
---|---|

Volume | 39 |

ISSN (Print) | 0169-7161 |

### Fingerprint

### 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

**The Life Table Population Identity : Discovery, Formulations, Proof, Extensions, and Applications.** / Carey, James R.; Silverman, Sarah; Rao, Arni S R.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Handbook of Statistics.*Handbook of Statistics, vol. 39, Elsevier B.V., pp. 155-186. https://doi.org/10.1016/bs.host.2018.08.002

}

TY - CHAP

T1 - The Life Table Population Identity

T2 - Discovery, Formulations, Proof, Extensions, and Applications

AU - Carey, James R.

AU - Silverman, Sarah

AU - Rao, Arni S R

PY - 2018/1/1

Y1 - 2018/1/1

N2 - 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.

AB - 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.

KW - Age-structure theorems

KW - Brouard's Theorem

KW - Carey's Equality

KW - Life table populations

KW - Nonstationary populations

KW - Stationary populations

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U2 - 10.1016/bs.host.2018.08.002

DO - 10.1016/bs.host.2018.08.002

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SN - 9780444640727

T3 - Handbook of Statistics

SP - 155

EP - 186

BT - Handbook of Statistics

A2 - Srinivasa Rao, Arni S.R.

A2 - Rao, C.R.

PB - Elsevier B.V.

ER -