On Fisher–Bhattacharyya Information Function and Lower Bounds under Right Random Censoring

In this paper, we prove that Fisher information in right random censoring can be decomposed by terms of a failure rate densities. Furthermore, we give an example that variance of unbiased estimate does not achieved Cramer–Rao lower bound, but the second order Bhattacharyya bound is attainable. For a special subfamily of exponential distribution in proportional hazard assumption prove that sequence of Bhattacharyya lower bounds tends to the variance of unbiased polynomial.

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