## Brazilian Journal of Probability and Statistics

### On the time-dependent Fisher information of a density function

#### Abstract

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.

#### Article information

Source
Braz. J. Probab. Stat., Volume 32, Number 4 (2018), 795-814.

Dates
Accepted: May 2017
First available in Project Euclid: 17 August 2018

https://projecteuclid.org/euclid.bjps/1534492902

Digital Object Identifier
doi:10.1214/17-BJPS366

Mathematical Reviews number (MathSciNet)
MR3845030

Zentralblatt MATH identifier
06979601

#### Citation

Kharazmi, Omid; Asadi, Majid. On the time-dependent Fisher information of a density function. Braz. J. Probab. Stat. 32 (2018), no. 4, 795--814. doi:10.1214/17-BJPS366. https://projecteuclid.org/euclid.bjps/1534492902

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