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.

Keyfitz熵指数是衡量预期寿命对死亡率变化敏感性的新指标。了解该指标的特征可以极大地帮助生命表研究进行生存分析。在本文中，我们仔细研究了Keyfitz熵指数的一些数学性质。首先，通过理论研究，我们发现在某些情况下该指数属于区间[0，1]，在其他情况下，该指数大于1。我们还使用Shannon熵和p为Keyfitz熵提供了两个不等式。随机变量的中心时刻。然后，我们为其提供经验值。该值可能有用，并且可以为研究人员提供有关Keyfitz熵值的初始信息，尤其是在使用常见的参数方法和非参数方法估计人口生存函数之前。其次，我们提出了一种新的非参数方法，该方法使用信息论来估计生命表中的生存函数，该理论应用了来自人口的现有信息，例如平均值和矩。通过这种方法估算的生存函数提供了Keyfitz熵的最大值，表明预期寿命对特定年龄死亡率的变化具有最大敏感性。