The difference between alternative averages

Vaupel, James W.; Zhang, Zhen

doi:10.4054/demres.2012.27.15

Cited by 3 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(1) of this paper for the special case a = 0) by using an alternative derivation from ours. Specifically, the author notes that e † (0) is equal to the gain in life expectancy from the revival from the first death, and further leverages Vaupel and Zhang (2012) results about how changes in weights affect means. The proof that we present in this paper provides a different approach to obtain the same relationship, while generalizing the relationship to all ages.…”

Section: Related Resultsmentioning

confidence: 99%

The Average Uneven Mortality index: Building on the "e-dagger" measure of lifespan inequality

Bonetti¹,

Basellini²,

Nigri³

2023

Preprint

View full text Add to dashboard Cite

In recent years, lifespan inequality has become an important indicator of population health, alongside more established longevity measures. Uncovering the statistical properties of lifespan inequality measures can provide novel insights on the study of mortality developments.We revisit the "e-dagger" measure of lifespan inequality, introduced in Vaupel and Canudas-Romo (2003). We note that, conditioning on surviving at least until age a, e-dagger(a) is equal to the covariance between the conditional lifespan random variable Ta and its transformation through its own cumulative hazard function (hence generalizing a result first noted in Schmertmann, 2020). We then derive an upper bound for e-dagger(a). Leveraging this result, we introduce the "Average Uneven Mortality" (AUM) index, a novel relative mortality index that can be used to analyze mortality patterns. We discuss some general features of the index, including its relationship with a constant ("even") force of mortality, and we study how it changes over time.The use of the AUM index is illustrated through an application to observed period and cohort death rates as well as to period life-table death rates from the Human Mortality Database. We explore the behavior of the index across age and over time, and we study its relationship with life expectancy. The AUM index at birth declined over time until the 1950s, when it reverted its trend. The index generally increases over age and reduces with increasing values of life expectancy, with differences between the period and cohort perspectives.We elaborate on Vaupel and Canudas-Romo’s e-dagger measure, deriving its upper bound. We exploit this result to introduce a novel mortality indicator, which enlarges the toolbox of available methods for the study of mortality dynamics. We also develop some new routines to compute e-dagger(a) and σ_Ta from death rates, and show that they have higher precision when compared to conventional and available functions, particularly for calculations involving older ages.

show abstract

Section: Related Resultsmentioning

confidence: 99%

The Average Uneven Mortality index: Building on the "e-dagger" measure of lifespan inequality

Bonetti¹,

Basellini²,

Nigri³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…x . Thus we can analyze G (0) using Vaupel and Zhang's (2012) result about how changes in weights affect means. Applying their main result to Equation (7) implies that (8)…”

Section: Life Expectancy Levels and Gains With R R R Revivalsmentioning

confidence: 99%

“…It is straightforward to generalize e † to second, third, and higher-order revivals by combining Equations. 3and 5and then applying Vaupel and Zhang's (2012) result about changing averages. A change from a regime with R revivals to one with R + 1 revivals will change life expectancy at birth by…”

Section: Life Expectancy Levels and Gains With R R R Revivalsmentioning

confidence: 99%