{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T20:12:13Z","timestamp":1771013533778,"version":"3.50.1"},"reference-count":32,"publisher":"Public Library of Science (PLoS)","issue":"2","license":[{"start":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T00:00:00Z","timestamp":1770940800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100007613","name":"Majmaah University","doi-asserted-by":"publisher","award":["IMSIU-DDRSP2502"],"award-info":[{"award-number":["IMSIU-DDRSP2502"]}],"id":[{"id":"10.13039\/501100007613","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["www.plosone.org"],"crossmark-restriction":false},"short-container-title":["PLoS One"],"abstract":"<jats:p>The analysis of inequalities aids in the formulation of optimal coding schemes that improve the rate of information transfer while reducing the probability of errors. This consequently implies that we have a major impact on having solid and secured correspondence systems for applications running from broadcast communications to information pressure. Information theory inequalities constitute a theoretical toolbox for designing channels that can overcome a challenging environment, allowing information to be held and communicated reliably and securely in a world that is becoming ever more interconnected. The paper introduces a general divergence model in general probability spaces and extends known information-theoretic inequalities and results based on variational models. We have built various inequalities for finite sequences of positive real numbers, the specific cases of which are important in information theory, especially in connection with several divergence models that remain in the literature. Additionally, we have derived certain other important communications concerning positive real numbers in relation to some divergence models.<\/jats:p>","DOI":"10.1371\/journal.pone.0341742","type":"journal-article","created":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T18:36:16Z","timestamp":1771007776000},"page":"e0341742","update-policy":"https:\/\/doi.org\/10.1371\/journal.pone.corrections_policy","source":"Crossref","is-referenced-by-count":0,"title":["Numerous inequalities and related communications accompanying discrete divergence models in probability spaces"],"prefix":"10.1371","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0287-7554","authenticated-orcid":true,"given":"Vikramjeet","family":"Singh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1732-2677","authenticated-orcid":true,"given":"Sunil Kumar","family":"Sharma","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Om","family":"Parkash","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0001-4088-6606","authenticated-orcid":true,"given":"Mona","family":"Bin-Asfour","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"340","published-online":{"date-parts":[[2026,2,13]]},"reference":[{"issue":"3","key":"pone.0341742.ref001","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":"CE Shannon","year":"1948","journal-title":"Bell Syst Tech J"},{"key":"pone.0341742.ref002","first-page":"547","author":"A Renyi","year":"1961","journal-title":"Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"pone.0341742.ref003","first-page":"30","article-title":"Quantification methods of classification process: Concept of structural \u03b1-entropy","volume":"3","author":"JH Havrada","year":"1967","journal-title":"Kybernetika"},{"issue":"3","key":"pone.0341742.ref004","doi-asserted-by":"crossref","first-page":"243","DOI":"10.3390\/e21030243","article-title":"Approximations of shannon mutual information for discrete variables with applications to neural population coding","volume":"21","author":"W Huang","year":"2019","journal-title":"Entropy (Basel)"},{"key":"pone.0341742.ref005","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.inffus.2019.12.010","article-title":"Theoretical analysis of Tsallis entropy-based quality measure for weighted averaging image fusion","volume":"58","author":"A Sholehkerdar","year":"2020","journal-title":"Inf Fusion"},{"key":"pone.0341742.ref006","doi-asserted-by":"crossref","first-page":"479","DOI":"10.1007\/BF01016429","article-title":"Possible generalization of Boltzmann-Gibbs statistics","volume":"52","author":"C Tsallis","year":"1988","journal-title":"J Stat Phys"},{"issue":"3","key":"pone.0341742.ref007","doi-asserted-by":"crossref","first-page":"368","DOI":"10.3390\/e22030368","article-title":"Entropy as a measure of attractiveness and socioeconomic complexity in rio de janeiro metropolitan area","volume":"22","author":"M Lenormand","year":"2020","journal-title":"Entropy (Basel)"},{"key":"pone.0341742.ref008","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1155\/2020\/4625218","article-title":"Entropy-based pattern learning based on singular spectrum analysis components for assessment of physiological signals","volume":"2020","author":"Y Lu","year":"2020","journal-title":"Complexity"},{"issue":"3","key":"pone.0341742.ref009","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1016\/j.kjs.2023.05.004","article-title":"On Shannon entropy and its applications","volume":"50","author":"P Saraiva","year":"2023","journal-title":"Kuwait J Sci"},{"issue":"5","key":"pone.0341742.ref010","doi-asserted-by":"crossref","first-page":"683","DOI":"10.3390\/e24050683","article-title":"Asymptotic normality for plug-in estimators of generalized shannon\u2019s entropy","volume":"24","author":"J Zhang","year":"2022","journal-title":"Entropy (Basel)"},{"issue":"3","key":"pone.0341742.ref011","doi-asserted-by":"crossref","first-page":"335","DOI":"10.3390\/e23030335","article-title":"Information measures for generalized order statistics and their concomitants under general framework from Huang-Kotz FGM bivariate distribution","volume":"23","author":"MA Abd Elgawad","year":"2021","journal-title":"Entropy (Basel)"},{"issue":"2","key":"pone.0341742.ref012","doi-asserted-by":"crossref","first-page":"121","DOI":"10.3390\/e26020121","article-title":"Maximum entropy criterion for moment indeterminacy of probability densities","volume":"26","author":"JM Stoyanov","year":"2024","journal-title":"Entropy (Basel)"},{"issue":"3","key":"pone.0341742.ref013","first-page":"273","article-title":"An uncertainty measure based on lower and upper approximations for generalized rough set models","volume":"166","author":"Z Wang","year":"2019","journal-title":"Fund Inform"},{"issue":"1","key":"pone.0341742.ref014","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1111\/j.2517-6161.1961.tb00404.x","article-title":"Inaccuracy and Inference","volume":"23","author":"DF Kerridge","year":"1961","journal-title":"J R Stat Soc Series B: Statistical Methodol"},{"issue":"6","key":"pone.0341742.ref015","doi-asserted-by":"crossref","first-page":"1446","DOI":"10.1080\/03610926.2019.1651859","article-title":"Estimation of past inaccuracy measure for the right censored dependent data","volume":"50","author":"EI Abdul Sathar","year":"2019","journal-title":"Commun Stat Theory Methods"},{"issue":"1","key":"pone.0341742.ref016","first-page":"1","article-title":"On the measures of errors in information","volume":"3","author":"P Nath","year":"1968","journal-title":"J Math Sci"},{"key":"pone.0341742.ref017","first-page":"57","article-title":"On the range of validity of certain measures of inaccuracy","volume":"5","author":"JN Kapur","year":"1987","journal-title":"Math Today"},{"key":"pone.0341742.ref018","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1016\/j.sigpro.2015.03.015","article-title":"Towards strongly consistent online HMM parameter estimation using one-step Kerridge inaccuracy","volume":"115","author":"TL Molloy","year":"2015","journal-title":"Signal Processing"},{"key":"pone.0341742.ref019","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1214\/aoms\/1177729694","article-title":"On information and sufficiency","volume":"22","author":"S Kullback","year":"1951","journal-title":"Ann Math Stat"},{"issue":"3","key":"pone.0341742.ref020","first-page":"3115","article-title":"New information theoretic models, their detailed properties and new inequalities","volume":"8","author":"O Parkash","year":"2014","journal-title":"Can J Pure Appl Sci"},{"issue":"2","key":"pone.0341742.ref021","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1007\/s00362-018-01082-8","article-title":"Bregman divergences based on optimal design criteria and simplicial measures of dispersion","volume":"60","author":"L Pronzato","year":"2019","journal-title":"Stat Pap"},{"issue":"2","key":"pone.0341742.ref022","doi-asserted-by":"crossref","first-page":"451","DOI":"10.7153\/jmi-2019-13-30","article-title":"Generalized \u2018useful\u2019 non-symmetric divergence measures and inequalities","volume":"13","author":"R Kumari","year":"2019","journal-title":"J Math Inequal"},{"key":"pone.0341742.ref023","doi-asserted-by":"crossref","first-page":"50","DOI":"10.1016\/j.ins.2019.09.033","article-title":"On the f-divergence for discrete non-additive measures","volume":"512","author":"V Torra","year":"2020","journal-title":"Inf Sci"},{"issue":"4","key":"pone.0341742.ref024","doi-asserted-by":"crossref","first-page":"909","DOI":"10.1080\/03610926.2018.1554123","article-title":"New definition of the cross entropy based on the Dempster-Shafer theory and its application in a decision-making process","volume":"49","author":"M Khalaj","year":"2019","journal-title":"Commun Stat Theory Methods"},{"issue":"2","key":"pone.0341742.ref025","doi-asserted-by":"crossref","first-page":"188","DOI":"10.3390\/e24020188","article-title":"Discriminant analysis under f-divergence measures","volume":"24","author":"A Dwivedi","year":"2022","journal-title":"Entropy (Basel)"},{"issue":"3","key":"pone.0341742.ref026","doi-asserted-by":"crossref","first-page":"421","DOI":"10.3390\/e24030421","article-title":"Statistical divergences between densities of truncated exponential families with nested supports: Duo bregman and duo jensen divergences","volume":"24","author":"F Nielsen","year":"2022","journal-title":"Entropy (Basel)"},{"key":"pone.0341742.ref027","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1007\/s41884-023-00122-z","article-title":"Estimation with infinite-dimensional exponential family and Fisher divergence","volume":"7","author":"K Fukumizu","year":"2024","journal-title":"Inf Geom"},{"issue":"208","key":"pone.0341742.ref028","doi-asserted-by":"crossref","first-page":"20230542","DOI":"10.1098\/rsif.2023.0542","article-title":"Mutation divergence over space in tumour expansion","volume":"20","author":"H Li","year":"2023","journal-title":"J R Soc Interface"},{"key":"pone.0341742.ref029","volume-title":"Information Theory","author":"R Ash","year":"1965"},{"key":"pone.0341742.ref030","volume-title":"Elements of Information Theory","author":"TM Cover","year":"1999"},{"key":"pone.0341742.ref031","volume-title":"Theory of Probability","author":"H Jeffreys","year":"1948"},{"key":"pone.0341742.ref032","first-page":"77","article-title":"Remarks on some measures of inaccuracy of finite discrete generalized probability distributions, entropy and ergodic theory","volume":"2","author":"P Nath","year":"1974","journal-title":"Selecta Stat Canad"}],"container-title":["PLOS One"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0341742","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,13]],"date-time":"2026-02-13T18:36:22Z","timestamp":1771007782000},"score":1,"resource":{"primary":{"URL":"https:\/\/dx.plos.org\/10.1371\/journal.pone.0341742"}},"subtitle":[],"editor":[{"given":"Fucai","family":"Lin","sequence":"first","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2026,2,13]]},"references-count":32,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2026,2,13]]}},"URL":"https:\/\/doi.org\/10.1371\/journal.pone.0341742","relation":{},"ISSN":["1932-6203"],"issn-type":[{"value":"1932-6203","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,13]]}}}