On the Fisher Information of Residual Lifetime

Let X be the lifetime of a system and Xt = (X − t|X > t) be the residual lifetime of the system at time t. In the present paper, we propose two dynamic measures to evaluate the dynamic Fisher information (DFI) and dynamic Fisher information distance (DFID) of residual lifetime Xt. We show that DFI and DFID of Xt are connected to well-known reliability measures such as hazard function (HF) and mean residual life (MRL). Several properties of DFI and DFDI are investigated based on aging properties of Xt