分位数框架下的分数阶累积过去不准确度及其应用
Fractional Cumulative Past Inaccuracy in the Quantile Framework and its Applications
- Cochin University of Science and Technology（科钦科技大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出基于分位数的分数阶累积过去不准确度及其动态版本，并给出性质、非参数估计器及实际应用。
AI中文摘要：
基于分数的信息度量在描述复杂系统方面受到了相当大的关注，因为它们能够以高灵敏度研究信号。在本文中，我们基于逆Mittag-Leffler函数（MLF）或分数对数函数，引入了分数阶累积过去不准确度（FCPI）和动态分数阶累积过去不准确度（DFCPI）的分位数版本，它们分别是分数阶累积过去熵和动态分数阶累积过去熵的扩展。我们提供了基于分位数的FCPI及其动态版本的各种性质。我们还为所提出的度量提出了一种非参数估计器，并进行了模拟研究以进行验证。最后，我们展示了新引入的基于分位数的FCPI的实际数据应用。
英文摘要：
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.
