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Abstract The mathematical derivations described in this paper offer a new look at the entropy of the life table, denoted by H. Contrary to previous claims, it is theoretically possible, and has been observed empirically, for life tables to have entropy values greater than unity. A re-expression of H as a weighted average of life expectancy at different ages relative to life expectancy at birth demonstrates clearly the conditions under which reductions in mortality by a fixed amount at all ages can result in even greater gains in life expectancy.
Goldman et al. (Thu,) studied this question.