期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2018
卷号：32
期号：4
页码：795-814
DOI：10.1214/17-BJPS366
语种：English
出版社：Brazilian Statistical Association
摘要：Fisher information is a very important and fundamental criterion in statistical inference especially in optimal and large sample studies in estimation theory. It also plays a key role in physics, thermodynamic, information theory and other applications. In the literature there have been defined two forms of Fisher information: one for the parameters of a distribution function and one for the density function of a distribution. In this paper, we consider a nonnegative continuous random (lifetime) variable $X$ and define a time-dependent Fisher information for density function of the residual random variable associated to $X$. We also propose a time-dependent version of Fisher information distance (relative Fisher information) between the densities of two nonnegative random variables. Several properties of the proposed measures and their relations to other statistical measures are investigated. To illustrate the results various examples are also provided.
