Time-dependent residual Fisher information and distance for some special continuous distributions

Abstract

Fisher information is a measure to quantify information and have important inferential, scaling and uncertainty properties. Kharazmi and Asadi (Braz. J. Prob. Stat. 32, 795-814, 2018) presented the time-dependent Fisher information of any density function. Specifically, they considered a nonnegative continuous random (lifetime) variable X and define the time-dependent Fisher information and distance for density function of the residual random variable associated to X. In this article, we computed the mentioned measures for generalized gamma, Beta prime, generalized inverse Gaussian and truncated skew-normal densities. For generalized gamma, beta prime and generalized inverse Gaussian densities, exact expressions are provided and, for truncated skew-normal case, we computed the mentioned measures for truncated (at positive support) skew-normal random variables by using exact expressions in terms of cumulants and moments. Some numerical results are illustrated.

Keywords:

• Beta prime
• Fisher information
• Generalized gamma
• Generalized inverse Gaussian
• Residual fisher information
• Truncated skew-normal

Acknowledgements

Contreras-Reyes’s research was funded by FONDECYT (Chile) grant No. 11190116. D. Gallardo acknowledge the support of Proyecto Gidi: “La estadística como respuesta a problemas de otras áreas” supported by the University of Atacama. The authors also thank the editor and two anonymous referees for their helpful comments and suggestions.