Special Collection 8
Formal Relationships
Published 20 January 2009
Special Collection 8 is an ongoing project containing short reports on mathematical relationships in formal demography. The collection was initiated by the journal’s founding publishers James W. Vaupel and Joshua R. Goldstein. It is currently being edited by Monica Alexander and Joshua R. Goldstein.
20 January 2009 | formal relationship
Formal Relationships: Introduction and Orientation
Volume: 20 Article ID: 1
Pages: 1–2
DOI: 10.4054/DemRes.2009.20.1
20 January 2009 | formal relationship
Life lived equals life left in stationary populations
Volume: 20 Article ID: 2
Pages: 3–6
DOI: 10.4054/DemRes.2009.20.2
20 January 2009 | formal relationship
Life lived and left: Carey’s equality
Volume: 20 Article ID: 3
Pages: 7–10
DOI: 10.4054/DemRes.2009.20.3
29 May 2009 | formal relationship
The effect of changes in fertility on the age distribution of stable populations
Volume: 20 Article ID: 24
Pages: 595–598
DOI: 10.4054/DemRes.2009.20.24
18 June 2009 | formal relationship
The age separating early deaths from late deaths
Volume: 20 Article ID: 29
Pages: 721–730
DOI: 10.4054/DemRes.2009.20.29
18 November 2009 | formal relationship
The metastable birth trajectory
Volume: 21 Article ID: 25
Pages: 759–764
DOI: 10.4054/DemRes.2009.21.25
11 December 2009 | formal relationship
Survival as a Function of Life Expectancy
Volume: 21 Article ID: 29
Pages: 879–884
DOI: 10.4054/DemRes.2009.21.29
22 January 2010 | formal relationship
Volume: 22 Article ID: 5
Pages: 115–128
DOI: 10.4054/DemRes.2010.22.5
30 June 2010 | formal relationship
Total daily change with age equals average lifetime change
Volume: 22 Article ID: 36
Pages: 1143–1148
DOI: 10.4054/DemRes.2010.22.36
09 July 2010 | formal relationship
Sensitivity of life disparity with respect to changes in mortality rates
Volume: 23 Article ID: 3
Pages: 63–72
DOI: 10.4054/DemRes.2010.23.3
07 September 2010 | formal relationship
Volume: 23 Article ID: 19
Pages: 531–548
DOI: 10.4054/DemRes.2010.23.19
12 October 2010 | formal relationship
Attrition in heterogeneous cohorts
Volume: 23 Article ID: 26
Pages: 737–748
DOI: 10.4054/DemRes.2010.23.26
08 February 2011 | formal relationship
Life expectancy: Lower and upper bounds from surviving fractions and remaining life expectancy
Volume: 24 Article ID: 11
Pages: 251–256
DOI: 10.4054/DemRes.2011.24.11
15 March 2011 | formal relationship
Linking period and cohort life-expectancy linear increases in Gompertz proportional hazards models
Volume: 24 Article ID: 19
Pages: 455–468
DOI: 10.4054/DemRes.2011.24.19
10 May 2011 | formal relationship
The reproductive value as part of the shadow price of population
Volume: 24 Article ID: 28
Pages: 709–718
DOI: 10.4054/DemRes.2011.24.28
10 June 2011 | formal relationship
Age-specific growth, reproductive values, and intrinsic r
Volume: 24 Article ID: 33
Pages: 825–830
DOI: 10.4054/DemRes.2011.24.33
18 April 2012 | formal relationship
Stationary populations with below-replacement fertility
Volume: 26 Article ID: 14
Pages: 319–330
DOI: 10.4054/DemRes.2012.26.14
06 March 2012 | formal relationship
Historical Addendum to "Life lived equals life left in stationary populations"
Volume: 26 Article ID: 7
Pages: 167–172
DOI: 10.4054/DemRes.2012.26.7
04 September 2012 | formal relationship
How life expectancy varies with perturbations in age-specific mortality
Volume: 27 Article ID: 13
Pages: 365–376
DOI: 10.4054/DemRes.2012.27.13
12 September 2012 | formal relationship
The difference between alternative averages
Volume: 27 Article ID: 15
Pages: 419–428
DOI: 10.4054/DemRes.2012.27.15
12 February 2013 | formal relationship
Gamma-Gompertz life expectancy at birth
Volume: 28 Article ID: 9
Pages: 259–270
DOI: 10.4054/DemRes.2013.28.9
06 May 2014 | formal relationship
Entropy of the Gompertz-Makeham mortality model
Volume: 30 Article ID: 49
Pages: 1397–1404
DOI: 10.4054/DemRes.2014.30.49
07 May 2014 | formal relationship
Variance in age at death equals average squared remaining life expectancy at death
Volume: 30 Article ID: 50
Pages: 1405–1412
DOI: 10.4054/DemRes.2014.30.50
16 May 2014 | formal relationship
Is the fraction of people ever born who are currently alive rising or falling?
Volume: 30 Article ID: 56
Pages: 1561–1570
DOI: 10.4054/DemRes.2014.30.56
29 April 2015 | formal relationship
Volume: 32 Article ID: 29
Pages: 827–834
DOI: 10.4054/DemRes.2015.32.29
20 May 2015 | formal relationship
The Gompertz force of mortality in terms of the modal age at death
Volume: 32 Article ID: 36
Pages: 1031–1048
DOI: 10.4054/DemRes.2015.32.36
19 August 2016 | formal relationship
Symmetries between life lived and left in finite stationary populations
Volume: 35 Article ID: 14
Pages: 381–398
DOI: 10.4054/DemRes.2016.35.14
27 September 2018 | formal relationship
Volume: 39 Article ID: 23
Pages: 671–684
DOI: 10.4054/DemRes.2018.39.23
26 October 2018 | formal relationship
Life lived and left: Estimating age-specific survival in stable populations with unknown ages
Volume: 39 Article ID: 37
Pages: 991–1008
DOI: 10.4054/DemRes.2018.39.37
09 July 2019 | formal relationship
The threshold age of the lifetable entropy
Volume: 41 Article ID: 4
Pages: 83–102
DOI: 10.4054/DemRes.2019.41.4
12 March 2020 | formal relationship
Revivorship and life lost to mortality
Volume: 42 Article ID: 17
Pages: 497–512
DOI: 10.4054/DemRes.2020.42.17
06 January 2021 | formal relationship
Born once, die once: Life table relationships for fertility
Volume: 44 Article ID: 2
Pages: 49–66
DOI: 10.4054/DemRes.2021.44.2
16 February 2021 | formal relationship
Volume: 44 Article ID: 15
Pages: 363–378
DOI: 10.4054/DemRes.2021.44.15
15 April 2021 | formal relationship
Outsurvival as a measure of the inequality of lifespans between two populations
Volume: 44 Article ID: 35
Pages: 853–864
DOI: 10.4054/DemRes.2021.44.35
11 June 2021 | formal relationship
Volume: 44 Article ID: 49
Pages: 1165–1184
DOI: 10.4054/DemRes.2021.44.49
17 May 2023 | formal relationship
Volume: 48 Article ID: 27
Pages: 809–828
DOI: 10.4054/DemRes.2023.48.27
19 January 2024 | formal relationship
The optimal transition to a stationary population for concentrated vitality rates
Volume: 50 Article ID: 6
Pages: 171–184
DOI: 10.4054/DemRes.2024.50.6