Abstract
In this work, we define the cumulative past Fisher (CPF) information and the relative cumulative past Fisher (RCRF) information measures for parameter as well as for the distribution function of the underlying random variables. We show that these cumulative past Fisher information measures can be expressed in terms of the reversed hazard rate function. We also define three extensions of the CPF information measure. Further, we study these cumulative information measures and their Bayes versions for some well-known models used in reliability, economics and survival analysis. The associated results reveal some interesting connections between the proposed Fisher type information measures with some well-known information divergences and reliability measures.
Acknowledgments
The authors express their sincere thanks to the Editor and the anonymous reviewers for their many useful comments and suggestions on an earlier version of this manuscript which let to this improvement version.
Citation
Narayanaswamy Balakrishnan. Omid Kharazmi. "Cumulative past Fisher information measure and its extensions." Braz. J. Probab. Stat. 36 (3) 540 - 559, September 2022. https://doi.org/10.1214/22-BJPS539
Information
