Volume 27 - Article 15 | Pages 419-428

The difference between alternative averages

By James Vaupel, Zhen Zhang

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Date received:17 Jul 2012
Date published:12 Sep 2012
Word count:1358
Keywords:covariance, population average, weighting function
Weblink:All publications in the ongoing Special Collection 8 "Formal Relationships" can be found at http://www.demographic-research.org/special/8/


Background: Demographers have long been interested in how compositional change, e.g., change in age structure, affects population averages.

Objective: We want to deepen understanding of how compositional change affects population averages.

Results: The difference between two averages of a variable, calculated using alternative weighting functions, equals the covariance between the variable and the ratio of the weighting functions, divided by the average of the ratio. We compare weighted and unweighted averages and also provide examples of use of the relationship in analyses of fertility and mortality.

Comments: Other uses of covariances in formal demography are worth exploring.

Author's Affiliation

James Vaupel - Max Planck Institute for Demographic Research, Germany [Email]
Zhen Zhang - Fudan University, China [Email]

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» The Gompertz force of mortality in terms of the modal age at death
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» Maternal longevity is associated with lower infant mortality
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» Unobserved population heterogeneity: A review of formal relationships
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» Attrition in heterogeneous cohorts
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» Senescence vs. sustenance: Evolutionary-demographic models of aging
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» Survival as a Function of Life Expectancy
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» The age separating early deaths from late deaths
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» Life lived and left: Carey’s equality
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» The relative tail of longevity and the mean remaining lifetime
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» Lifesaving, lifetimes and lifetables
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» Oldest Old Mortality in China
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» Life Expectancy at Current Rates vs. Current Conditions: A Reflexion Stimulated by Bongaarts and Feeney’s "How Long Do We Live?"
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» Dr. Väinö Kannisto: A Reflexion
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»Volume 27





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