Some aspects of reversed hazard rate and past entropy

The entropy of past lifetime is closely related to the reversed hazard rate. Since the reversed hazard rate of a non negative random variable with an absolutely continuous distribution can neither be constant nor monotonic increasing on the positive real line, there are limitations on deriving vario...

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Bibliographic Details
Published in:Communications in statistics. Theory and methods 2021-05, Vol.50 (9), p.2106-2116
Main Authors: Unnikrishnan Nair, N., Sunoj, S. M., G., Rajesh
Format: Article
Language:English
Subjects:
characterizations
Continuity (mathematics)
decreasing uncertainty of past life
Entropy
Increasing and bathtub shaped reversed hazard rates
past entropy
Random variables
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Summary:The entropy of past lifetime is closely related to the reversed hazard rate. Since the reversed hazard rate of a non negative random variable with an absolutely continuous distribution can neither be constant nor monotonic increasing on the positive real line, there are limitations on deriving various properties of past entropy as well. In this work we investigate conditions under which reversed hazard rate can be increasing and can assume different non monotone shapes and use them to derive some new classes of past entropy-based life distributions and characterizations.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2019.1659970