Volume 49 - Article 1 | Pages 1–12  

On a closed-form expression and its approximation to Gompertz life disparity

By Cinzia Di Palo

Abstract

Background: In the literature, there exists a closed form solution to the remaining life expectancy at age x when mortality is governed by the Gompertz law. This expression contains a special function that allows us to construct high-accuracy approximations, which are also helpful in assessing the elasticity of life expectancy with respect to the model parameters. However, to my knowledge, a similar formulation for life disparity does not exist, and as a consequence, it does not exist for life table entropy either.

Contribution: Under the assumption that mortality is governed by the Gompertz law, I present and prove a closed form expression for life disparity at age x that is similar to that existing for life expectancy. Since the closed form expressions hold for both life expectancy and life disparity, an exact expression for the life table entropy is immediately derived. In addition, using known relationships on the exponential integral function, an approximate form for life disparity is also obtained.

Author's Affiliation

• Cinzia Di Palo - Università degli Studi di Cassino e del Lazio Meridionale, Italy EMAIL

Most recent similar articles in Demographic Research

Racial classification as a multistate process
Volume 50 - Article 17    | Keywords: Brazil, demography, increments to life, life expectancy, life table, mortality, multistate, race/ethnicity

Proximity to mother over the life course in the United States: Overall patterns and racial differences
Volume 45 - Article 23    | Keywords: family, geographical proximity, intergenerational relationships, life course, life table, panel studies, race/ethnicity, spatial availability

Distributionally adjusted life expectancy as a life table function
Volume 43 - Article 14    | Keywords: duration, inequality, length of life, life expectancy, life table

The impact of the choice of life table statistics when forecasting mortality
Volume 41 - Article 43    | Keywords: life expectancy, life table, mortality forecasts, rate of mortality improvement

The magnitude and timing of grandparental coresidence during childhood in the United States
Volume 37 - Article 52    | Keywords: family structure, grandfamilies, grandparents, life table, multigenerational households, three-generation families, United States of America