2023/07/26 by Marco Capaldo, Antonio Di Crescenzo, Capaldo, Marco +3
Decision Sciences · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #Probabilistic and Robust Engineering Design #Probability (math.PR) #Reliability and Maintenance Optimization #Statistical Distribution Estimation and Applications #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.2307.14290
openalex publication_date 2023/07/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We introduce and study the cumulative information generating function, which provides a unifying mathematical tool suitable to deal with classical and fractional entropies based on the cumulative distribution function and on the survival function. Specifically, after establishing its main properties and some bounds, we show that it is a variability measure itself that extends the Gini mean semi-difference. We also provide (i) an extension of such a measure, based on distortion functions, and (ii) a weighted version based on a mixture distribution. Furthermore, we explore some connections with the reliability of k-out-of-n systems and with stress-strength models for multi-component systems. Also, we address the problem of extending the cumulative information generating function to higher dimensions.