Local Weibull model and its application to life expectancy estimation

Abstract

In a previous article, we have introduced a model to study life expectancy based on a sequence of Weibull distributions. Each of these distributions characterizes the living expectancy within a certain age interval. In the second step, we estimate the parameters for this model by combining the moment estimations and censoring methods. We have named this combination “the local parametric estimation method”. In this article, we present a different model that requires less number of random variable characteristics which help alleviate the estimation procedure. In fact, in comparison with the previous model, we are able to obtain an explicit formula for the variance of life expectancy. This is particularly useful in obtaining a normal approximation to life expectancy. Extensive computations with real-world datasets show that the local parametric method provides less biased estimation with lower variance in comparison to the Chiang method. This fact allows one to use statistical tests to detect life expectancy estimation differences as shown in the data where the Chiang method does not perform well. Additionally, the new life expectancy estimation method is also useful in the assessment of the health inequality in small area/small population settings by conducting statistical tests.