How do you assess inequality in the distribution of life expectancy at birth?
Life expectancy is calculated as the average life span of a hypothetical cohort of 100,000 people born at the same time who progress through successive ages, with the cohort shrinking from one age to the next according to a set of age-specific death rates, until all people in the cohort die. Such an average is the life span that people born in the same year can be expected to live under the constant-mortality assumption, i.e., age-specific mortality is maintained constant throughout the life of the cohort at the level estimated for the reference year of birth or the reference period.
As the cohort shrinks from one age to the next, it implies that people from the cohort are dying at different ages – thus there is an inequality in life spans. We capture this inequality and use it as the inequality measure of the health dimension - in the same way as we use the average of these life spans (i.e., life expectancy) to estimate the average achievement in health dimension.