What is it about?
This study extends the concept of cumulative residual inaccuracy (CRI)—an information-theoretic measure that quantifies the inaccuracy between two probability models—to the framework of k-record values. In probability theory, record values represent successive extreme observations in a sequence of random variables. The notion of k-record values generalizes this idea by considering not only the maximum observations but also the second, third, and higher-order extremes. By formulating the CRI for such -record structures, the paper broadens the applicability of inaccuracy-based measures to situations where record-type or extreme-value data are of interest. The work establishes mathematical properties, inequalities, and stochastic ordering relations for the proposed measure and provides explicit results for standard probability distributions. These results enhance the theoretical foundations of inaccuracy-based entropy measures and support their use in reliability analysis, risk modeling, and other areas of science and engineering concerned with extremal behavior.
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Why is it important?
This study which involves practical concerns of forecasting for e.g. insurance claims has connections to Science.
Perspectives
It's a matter of practical applications in particular, measure of risk, forecasting in insurance claims and possibly Fintech.
Dr Tony Cyril Scott
RWTH-Aachen University
Writing this article was a great pleasure as it has co-authors with whom I have had long standing collaborations
Sarang Vehale
National Forensic Sciences University
This research is important because it improves how we measure and understand errors or differences between probability models when we are dealing with extreme events. In many real-life situations—such as system failures, financial crashes, floods, or maximum stress on materials—we are not interested in average behavior, but in record-breaking or extreme values.
Dr. Ritu Goel
Read the Original
This page is a summary of: Some Results on Cumulative Residual Inaccuracy Measure of k-Record Values, Entropy, December 2025, MDPI AG,
DOI: 10.3390/e28010017.
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