Keyfitz entropy: investigating some mathematical properties and its application for estimating survival function in life table

Abstract

Keyfitz entropy index is a new indicator that measures the sensitivity of life expectancy to a change in mortality rate. Understanding the characteristics of this indicator can significantly help life table studies in survival analysis. In this paper, we take a closer look at some mathematical properties of Keyfitz entropy index. First, using theoretical studies we show that in some cases this index belongs to the interval [0, 1] and in other cases, it is greater than 1. We also provide two inequalities for Keyfitz entropy using Shannon entropy and pth central moments of random variables. Then, we present an empirical value for it. This value can be useful and provides initial information about Keyfitz entropy value to the researcher, especially before estimating the population survival function with common parametric and nonparametric methods. Second, we propose a new nonparametric method for estimating the survival function in life table using information theory which applies existing information from the population, such as average and moments. The survival function estimated by this method provides the maximum value for Keyfitz entropy indicating the maximum sensitivity of life expectancy to changes in age-specific mortality rates. We also demonstrate that the survival function estimated by this method can be a powerful competitor to its counterparts which are estimated by common parametric and nonparametric methods.