{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T05:39:40Z","timestamp":1766986780359,"version":"3.48.0"},"reference-count":33,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2025,12,26]],"date-time":"2025-12-26T00:00:00Z","timestamp":1766707200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100009392","name":"Prince Sattam bin Abdulaziz University","doi-asserted-by":"publisher","award":["PSAU\/2025\/02\/37509"],"award-info":[{"award-number":["PSAU\/2025\/02\/37509"]}],"id":[{"id":"10.13039\/100009392","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The entropy measure of residual cumulative Sharma\u2013Taneja\u2013Mittal is an alternative measure of uncertainty for residual cumulative entropy. This study investigates further theoretical properties and develops nonparametric estimation procedures for the proposed measure. The performance of the estimator is evaluated through simulation experiments, and its practical relevance is illustrated using a real-world dataset on malignant tumor cases. Moreover, we investigate the properties of its dynamic version, including stochastic comparisons and its connections with the hazard rate function, mean residual function, and equilibrium random variables. Moreover, we introduce an alternative version of dynamic residual cumulative Sharma\u2013Taneja\u2013Mittal entropy and examine its monotonic properties. Additionally, we discuss this alternative version and its conditional form in the circumstances of record values. We introduce this alternative expression for the residual lifespan of upper record quantities in general distributions, characterizing it as a measure of upper record quantities derived from a distribution of uniform. Since Sharma\u2013Taneja\u2013Mittal entropy measures uncertainty, we also investigate its use in determining the entropy of the lifespan of mixed and coherent mechanisms, in which the lives of its constituent components are identically distributed and independent.<\/jats:p>","DOI":"10.3390\/e28010032","type":"journal-article","created":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T05:28:19Z","timestamp":1766986099000},"page":"32","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Properties of Residual Cumulative Sharma\u2013Taneja\u2013Mittal Model and Its Extensions in Reliability Theory with Applications to Human Health Analysis and Mixed Coherent Mechanisms"],"prefix":"10.3390","volume":"28","author":[{"given":"Mohamed Said","family":"Mohamed","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University, Hawtat Bani Tamim 16511, Saudi Arabia"}]},{"given":"Hanan H.","family":"Sakr","sequence":"additional","affiliation":[{"name":"Department of Management Information Systems, College of Business Administration in Hawtat Bani Tamim, Prince Sattam bin Abdulaziz University, Al-Kharj 16273, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,12,26]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1002\/j.1538-7305.1948.tb01338.x","article-title":"A mathematical theory of communication","volume":"27","author":"Shannon","year":"1948","journal-title":"Bell Syst. Tech. J."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1220","DOI":"10.1109\/TIT.2004.828057","article-title":"Cumulative residual entropy: A new measure of information","volume":"50","author":"Rao","year":"2004","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0167-7152(00)00056-0","article-title":"Residual entropy and its characterizations in terms of hazard function and mean residual life function","volume":"49","author":"Asadi","year":"2000","journal-title":"Stat. Probab. Lett."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1931","DOI":"10.1016\/j.jspi.2006.06.035","article-title":"On the dynamic cumulative residual entropy","volume":"137","author":"Asadi","year":"2007","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"310","DOI":"10.1016\/j.jspi.2009.07.015","article-title":"Some new results on the cumulative residual entropy","volume":"140","author":"Navarro","year":"2010","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_6","first-page":"48","article-title":"How to measure uncertainty in the residual lifetime distribution","volume":"58","author":"Ebrahimi","year":"1996","journal-title":"Sankhya Ser. A"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"85","DOI":"10.1016\/j.spl.2004.10.033","article-title":"Dynamic generalized information measures","volume":"71","author":"Asadi","year":"2005","journal-title":"Stat. Probab. Lett."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/j.ins.2004.10.008","article-title":"Some results on generalized residual entropy","volume":"176","author":"Nanda","year":"2006","journal-title":"Inf. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1007\/s11005-007-0155-1","article-title":"Uniform estimates on the Tsallis entropies","volume":"80","author":"Zhang","year":"2007","journal-title":"Lett. Math. Phys."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1007\/BF01899728","article-title":"Entropy of type (\u03b1,\u03b2) and other generalized measures in information theory","volume":"22","author":"Sharma","year":"1975","journal-title":"Metrika"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/BF01899712","article-title":"On some functional equations concerning entropy, directed divergence and inaccuracy","volume":"22","author":"Mittal","year":"1975","journal-title":"Metrika"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"Tsallis","year":"1988","journal-title":"J. Stat. Phys."},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Kattumannil, S.K., Sreedevi, E.P., and Balakrishnan, N. (2022). A Generalized Measure of Cumulative Residual Entropy. Entropy, 24.","DOI":"10.20944\/preprints202202.0322.v1"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1017\/S026996482200047X","article-title":"Relationships between cumulative entropy\/extropy, Gini mean difference and probability weighted moments","volume":"38","author":"Sudheesh","year":"2024","journal-title":"Probab. Eng. Inf. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","unstructured":"Sakr, H.H., and Mohamed, M.S. (2024). Sharma-Taneja-Mittal Entropy and Its Application of Obesity in Saudi Arabia. Mathematics, 12.","DOI":"10.3390\/math12172639"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/s10714-019-2578-2","article-title":"Black hole thermodynamics in Sharma-Mittal generalized entropy formalism","volume":"51","author":"Ghaffari","year":"2019","journal-title":"Gen. Relativ. Gravit."},{"key":"ref_17","doi-asserted-by":"crossref","unstructured":"Koltcov, S., Ignatenko, V., and Koltsova, O. (2019). Estimating topic modeling performance with Sharma- Mittal entropy. Entropy, 21.","DOI":"10.3390\/e21070660"},{"key":"ref_18","first-page":"273","article-title":"Sharma-Mittal entropy properties on record values","volume":"76","author":"Paul","year":"2016","journal-title":"Statistica"},{"key":"ref_19","first-page":"125","article-title":"An alternate measure of the cumulative residual Sharma-Taneja-Mittal entropy","volume":"33","author":"Sfetcu","year":"2025","journal-title":"An. St. Univ. Ovidius Constanta Ser. Mat."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1214\/aoms\/1177729639","article-title":"Consistency and unbiasedness of certain nonparametric tests","volume":"22","author":"Lehmann","year":"1951","journal-title":"Ann. Math. Stat."},{"key":"ref_21","unstructured":"Lee, A.J. (2019). U-Statistics: Theory and Practice, Routledge."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Arnold, B.C., Balakrishnan, N., and Nagaraja, H.N. (2008). A First Course in Order Statistics, SIAM.","DOI":"10.1137\/1.9780898719062"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"3660","DOI":"10.1016\/j.jspi.2007.11.014","article-title":"On the mean residual life of records","volume":"138","author":"Raqab","year":"2008","journal-title":"J. Stat. Plan. Inference"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Shaked, M., and Shanthikumar, J.G. (2007). Stochastic Orders, Springer.","DOI":"10.1007\/978-0-387-34675-5"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Samaniego, F.J. (2007). System Signatures and Their Applications in Engineering Reliability, Springer Science and Business Media.","DOI":"10.1007\/978-0-387-71797-5"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1377","DOI":"10.1080\/03610928608829189","article-title":"On tail-ordering and comparison of failure rates","volume":"15","author":"Bagai","year":"1986","journal-title":"Commun. Stat.-Theory Methods"},{"key":"ref_27","unstructured":"Cover, T.M., and Thomas, J.A. (2012). Elements of Information Theory, Wiley."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"4868","DOI":"10.1063\/1.1805729","article-title":"Fundamental properties of Tsallis relative entropy","volume":"45","author":"Furuichi","year":"2004","journal-title":"J. Math. Phys."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1016\/S0378-4371(01)00184-4","article-title":"Non-linear kinetics underlying generalized statistics","volume":"296","author":"Kaniadakis","year":"2001","journal-title":"Phys. A"},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Mohamed, M.S., and Sakr, H.H. (2025). Uniformity Testing and Estimation of Generalized Exponential Uncertainty in Human Health Analytics. Symmetry, 17.","DOI":"10.3390\/sym17091403"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Mohamed, M.S., and Sakr, H.H. (2025). Generalizing Uncertainty Through Dynamic Development and Analysis of Residual Cumulative Generalized Fractional Extropy with Applications in Human Health. Fractal Fract., 9.","DOI":"10.3390\/fractalfract9060388"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Principes, J.C. (2010). Information Theoretic Learning R\u00e9nyi\u2019s Entropy and Kernel Perspectives, Springer Science Business Media LLC.","DOI":"10.1007\/978-1-4419-1570-2"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.physa.2016.04.017","article-title":"Tsallis and R\u00e9nyi divergences of generalized Jacobi polynomials","volume":"460","author":"Sfetcu","year":"2016","journal-title":"Phys. A"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/1\/32\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,29]],"date-time":"2025-12-29T05:36:16Z","timestamp":1766986576000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/1\/32"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,12,26]]},"references-count":33,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2026,1]]}},"alternative-id":["e28010032"],"URL":"https:\/\/doi.org\/10.3390\/e28010032","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,12,26]]}}}