A generalization of life expectancy which incorporates the age distribution of the population and its use in the measurement of the impact of mortality reduction

Two new families of indices measuring the gain in life expectancy resulting from reduction in mortality are introduced: the first looks at the impact of cause of death reduction from the perspective of the entire population; the second, at that segment of the population due to die of the cause. Special cases include both well-established measures and extensions that incorporate the age distribution of the population. A further generalization is introduced with the consideration of life expectancies that only give weight to years of life up to age 70. A number of inequalities are derived that relate cause-deleted life expectancies to their cause-reduced counterparts.