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PreprintCC0arXiv

Fractional Cumulative Past Inaccuracy in the Quantile Framework and its Applications

  • Iona Ann Sebastian
  • S. M. Sunoj
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Abstract

Fraction-based information measures have received considerable attention for describing complex systems, as they enable the investigation of signals with high sensitivity \citep{machado2014fractional}. In this paper, we introduce quantile versions of fractional cumulative past inaccuracy (FCPI) and dynamic fractional cumulative past inaccuracy (DFCPI) measures based on the inverse Mittag-Leffler function (MLF) or fractional logarithm function, which are the extensions of the fractional cumulative past and dynamic fractional cumulative past entropies, respectively. The various properties of quantile-based FCPI and its dynamic version are provided. We also propose a nonparametric estimator for the proposed measure, and simulation studies are carried out for validation. Finally, we bring out real data application of the newly introduced quantile-based FCPI.

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Cite

BibTeXRIS
BibTeX
@misc{sebastian2026fractional,
  title = {{Fractional Cumulative Past Inaccuracy in the Quantile Framework and its Applications}},
  author = {Iona Ann Sebastian and S. M. Sunoj},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.15204},
  eprint = {2609.15204},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.15204},
  note = {CC0},
}
RIS
TY  - UNPB
TI  - Fractional Cumulative Past Inaccuracy in the Quantile Framework and its Applications
AU  - Iona Ann Sebastian
AU  - S. M. Sunoj
PY  - 2026
DA  - 2026/09/14
PB  - arXiv
DO  - 10.48550/arxiv.2609.15204
UR  - https://arxiv.org/abs/2609.15204
AB  - Fraction-based information measures have received considerable attention for describing complex systems, as they enable the investigation of signals with high sensitivity \citep{machado2014fractional}. In this paper, we introduce quantile versions of fractional cumulative past inaccuracy (FCPI) and dynamic fractional cumulative past inaccuracy (DFCPI) measures based on the inverse Mittag-Leffler function (MLF) or fractional logarithm function, which are the extensions of the fractional cumulative past and dynamic fractional cumulative past entropies, respectively. The various properties of quantile-based FCPI and its dynamic version are provided. We also propose a nonparametric estimator for the proposed measure, and simulation studies are carried out for validation. Finally, we bring out real data application of the newly introduced quantile-based FCPI.
ER  -