Fractional Cumulative Past Inaccuracy in the Quantile Framework and its Applications

RESUMO

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.