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PreprintCC BY 4.0arXiv

Nonparametric Inference for Cumulative Residual Mathai--Haubold Entropy of order α

  • Anija C. R
  • Smitha
  • S.
  • Sudheesh
  • K. Kattumannil
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Abstract

In this paper, we study the properties of cumulative residual Mathai--Haubold entropy of order α. A dynamic version of this entropy measure is then proposed, and its properties are examined within the framework of reliability modeling. We show that the dynamic cumulative residual Mathai--Haubold entropy of order α uniquely determines the survival function. Characterization results for the exponential and generalized Pareto distributions are derived using the proposed measure. Furthermore, we develop nonparametric estimators for the cumulative residual Mathai--Haubold entropy and its dynamic counterpart of order α, based on the kernel estimation of the survival function. The performance of these estimators is evaluated through a Monte Carlo simulation study. Finally, the practical relevance of the proposed dynamic estimator is illustrated using two real data; failure-time data from aircraft windshields and failure-time data from 40 randomly selected mechanical switches.

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Cite

BibTeXRIS
BibTeX
@misc{c2026nonparametric,
  title = {{Nonparametric Inference for Cumulative Residual Mathai--Haubold Entropy of order $α$}},
  author = {Anija C. R and Smitha and S. and Sudheesh and K. Kattumannil},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.08434},
  eprint = {2609.08434},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.08434},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Nonparametric Inference for Cumulative Residual Mathai--Haubold Entropy of order α
AU  - Anija C. R
AU  - Smitha
AU  - S.
AU  - Sudheesh
AU  - K. Kattumannil
PY  - 2026
DA  - 2026/09/08
PB  - arXiv
DO  - 10.48550/arxiv.2609.08434
UR  - https://arxiv.org/abs/2609.08434
AB  - In this paper, we study the properties of cumulative residual Mathai--Haubold entropy of order α. A dynamic version of this entropy measure is then proposed, and its properties are examined within the framework of reliability modeling. We show that the dynamic cumulative residual Mathai--Haubold entropy of order α uniquely determines the survival function. Characterization results for the exponential and generalized Pareto distributions are derived using the proposed measure. Furthermore, we develop nonparametric estimators for the cumulative residual Mathai--Haubold entropy and its dynamic counterpart of order α, based on the kernel estimation of the survival function. The performance of these estimators is evaluated through a Monte Carlo simulation study. Finally, the practical relevance of the proposed dynamic estimator is illustrated using two real data; failure-time data from aircraft windshields and failure-time data from 40 randomly selected mechanical switches.
ER  -